How many languages do Willie and Modesty speak? Here is the evidence.

French

In Le Gant Rouge the agent of La Machine complains: "Why the devil must Garvin talk in that Cockney English when he speaks French like a Parisien."
(La Machine, panel 46)

She struggled to pull free for a moment, then gave up and burst into a torrent of French.
‘Je n’ai rien fait, Willie! Rien, je te dis …’ Tarrant could barely follow the rapid gabble.
Willie cut her short in the same language. ‘Tais-toi, petite voleuse!’
(Sabre-Tooth, Chapter 2)

Ransome’s [Willie's] French was fluent but with no rhythm or inflexion except for the American twang and the Anglo-Saxon vowels which grated on the Director’s nerves.
(Sabre-Tooth, Chapter 8)

Modesty and Willie use French when meeting Nedic in Yugoslavia.
(I, Lucifer, chapter 9)

She heard a gruff voice speak with rising astonishment. ‘Il y-a quelqu’un là dedans?’
She could manage only a husky whisper as she said in French, ‘M’sieu, I am trapped in a cave behind this boulder. Can you hear me?’
...
‘Enchanted to make your acquaintance, mam’selle. You speak very good French.’
(Old Alex)

Spanish

Willie staggers into the rebel group executing Diana Millard, speaking Spanish but taken for a foreigner.
(The Green-eyed Monster, panel 2335)

'José raised a hand in welcome. Both Señor Garvin and the dark girl [Modesty] spoke good Spanish and were pleasant companions to gossip with.'
(Last Day in Limbo , chapter 8)

Modesty and Willie use Spanish with the various officers and soldiers of San Lucero in Maluque.
(The Inca Trail, e.g. panel 4000)

Modesty receives a telegram from Venezuela in Spanish which Weng reads aloud to her.
(A Few Flowers for the Colonel, panel 5428)

(Willie is given a 15-page document to read.) ‘It was in Spanish, but she already knew he spoke four languages including Arabic with fair fluency and had a smattering of two more.’
(Bellman)

Willie said quietly in Spanish: ‘Do not be afraid, señorita. You will not be hurt.’ The needle went into her buttock and she gasped, head turned to glare back at him with mingled rage and shock, both transformed to bewilderment as he went on reassuringly, ‘Let us count backwards from ten to one, señorita. It prevents insomnia.’
(Bellman)

Willie has lost his memory, but responds to Rima, the girl who has rescued him from the river, in Spanish.
(A Present for the Princess, panel 8093)

Bandit: You speak Spanish?
Willie: I speak a little Spanish, señor.
Later Willie is recognised.
Durango: You both speak good Spanish, so you understand the order I just gave.
(Durango, panels 8049a and 8054a)

Arabic

‘Your Highness,’ Tarrant said with a slight bow. ‘Allow me to present Modesty Blaise.’
Abu-Tahir’s eyes rested on Modesty, twinkling. He touched a hand to his forehead and to his heart.
‘Salam alêkum, sayyide.’
Modesty’s hand moved in the same gesture. ‘Nehârkum sa’id we-mubârek.’
‘Awhashtena.’
Tarrant knew that one. “You have made us lonely.” Again he was puzzled.
‘Allâh ma yûhishek,’ said Modesty.
(Modesty Blaise, chapter 6)

‘Willie Garvin was still closer now. The patch of sand had been carefully smoothed and its surface bore a few squiggles, as if someone had doodled on it with a finger. The squiggles were Arabic words.’
(I, Lucifer, chapter 17)

The same technique is used when Modesty leaves Willie's unconscious body on the sand on Moggairne Island.
(The Grim Joker, panel 8348)

‘The old Arabic,’ said Willie. ‘Coming on a treat, too. I reckon I’ll be as good as you by the time I get ’ome.’
Modesty relaxed. ‘That’s fine. I seem to remember you were having a lot of trouble with that long poem by Sa’ad.’
‘I’ve got if off by ’eart now.’ There was pride in Willie’s voice. ‘Listen…’ He began to speak another language, rhythmically but with occasional hesitations.
…
‘How was that, then?’ Willie ended.
‘Not bad. You’ve been practising your accent. But that second stanza wasn’t quite right. It should go—’ She broke into Arabic for a few seconds, then added, ‘Got it?’
(A Taste for Death, Chapter 4)

The guards he had seen were city Algerian, if his guess was right. They spoke no English, a little French. Their language was Arabic, which Modesty and Willie spoke fluently.
(A Taste for Death, Chapter 13)

Willie Garvin uses a miniature transmitter to talk to Modesty for twenty minutes from inside the Wilderness Estate, using Arabic.
(Highland Witch, panel 3521)

When talking to Sheikh Kadhim on the telephone, Modesty begins in English but suggests switching to Arabic when putting forward her plan.
(The Vanishing Dollybirds, panel 4109)

Modesty uses Arabic to communicate with Willie from her prison cell.
(Death Trap, panels 4307-8)

“… And when we talked this morning we used Arabic, so it’s long odds against being understood by anyone roaming the amateur frequencies.”
(Dragon’s Claw, chapter 3)

“… Name of Sam Solon.” She switched to Arabic. “He was on our list of possibles back in The Network days, remember?” …
(Dragon’s Claw, chapter 3)

Then had come the storm, and when it was over Blaise and Garvin had talked mainly in Arabic. This had seemed ominous, but when Fouad, one of Condori’s guards, had been called in to translate the tape recording, it became clear that Dr. Feng’s memory blocks had held firm, and Luke Fletcher had told her no more than that he was Luke Fletcher. The only reason for secrecy in the transmission was Modesty Blaise’s wish to avoid publicity.
(Dragon’s Claw, chapter 4)

Sir Gerald: I'm most grateful to you—it was quite as boring as most functions…but our Arab guest of honour enjoyed talking to you in his own language.
Modesty: Nice to be of use to you without losing any skin, Sir Gerald.
(Idaho George, panel 4360)

The tunnel grew lighter, hotter, the murmur of the outside world grew clearer, then at last the sun struck down upon her head and she had to close her eyes against its brightness. A pause, two or three voices, the sound of movement. Willie saying in Arabic, “Gently … gently with the stretcher.”
(The Xanadu Talisman, chapter 2)

Fluent in Arabic and knowing the Middle East well, Willie Garvin had still been stunned by the unbelievable opulence he had seen.
(The Xanadu Talisman, chapter 8)

Willie talks to Weng in Arabic when calling from Athens.
(Plato's Republic, panel 6082)

He [Willie] gave me [Modesty] the whole story in a mixture of free cryptic and Arabic, but I had no ideas to offer.
(Dead Man's Handle, chapter 2)

Mr J: Who were these tourists? [Willie and Modesty]
Robber: We do not know, Mr. J. To us they spoke Arabic—to each other English.
...
Fiama: You are English, I think. Yet you both speak well in my tongue.
Modesty: We lived in Tangier for some years.
(Tribute of the Pharaohs,, panels 9374a and 9386)

Chinese

Modesty talks to Weng in Cantonese when calling from Voulakis Island.
(Plato's Republic, panel 6080)

Willie Garvin strolled across the compound towards the fuel store, pausing to hawk and spit noisily when he was close enough to make out the figure of the sentry there. No challenge came, only a few casual words in Chinese, perhaps asking a comrade soldier for a cigarette or a light. Willie Garvin grunted a wordless reply …
(Dead Man’s Handle , chapter 1)

… every time we ’it a pot-hole he kept praying in Chinese. Well, I think it was praying …
(Dead Man’s Handle , chapter 1)

As the last word left her lips she was reaching for the dial to change frequency, turning it to the twenty metre band, then turning to fourteen one-o-three megs. Seconds later she began to speak in Cantonese.
(Dead Man’s Handle , chapter 13)

“She [Modesty] was speaking in a Chinese sounding language when Mr. Kypseli came to his senses, I understand,” said Thaddeus Pilgrim musingly. “But one cannot say Kalivari in Chinese, can one? Did Mr. Kypseli hear this word?”
(Dead Man’s Handle , chapter 13)

Weng to Tarrant “ I am to tell you that when I report to Miss Blaise [in Transylvania] by radio I shall do so in Cantonese and cryptically.”
(The Vampire of Malvescu, panel 6779a)

Greek

Tarrant speaks to Professor Carson on the telephone using classical Greek to avoid eavesdropping. “Not totally secure, but good enough, I fancy.”
(Take me to your Leader, panel 3332)

She [Modesty] spoke to him in Greek, but apart from telling her to follow him he made no response. … The younger of the two fishermen, who had brought her down from the cliff, said to the other, “She speaks Greek.”
(Dead Man's Handle, chapter 8)

German

They [Willie and Modesty] were drinking beer and speaking very quietly in German. The waiter thought they were from one of the German technical contingents in the area.
(Modesty Blaise, chapter 13)

In The Giggle-wrecker, Modesty and Willie play the part of Swedish antique dealers buying stock in East Germany. This implies good command of German.

Italian

She [Modesty] looked at him and said in Italian: ‘The name is Forli, isn’t it?’
(Sabre-tooth, Chapter 10)

The child stopped crying and asked a question in the heavily accented Greek of one of the small islands. Modesty Blaise stopped, looked towards the Sicilian, who sat with her arm about the child, and said softly in Italian, “Keep the little one quiet and don’t wake the others. All things will be better soon.”
(The Night of Morningstar, chapter 2)

In a café in Venice, Willie speaks to Modesty in Italian in order to be overheard by the waitress Oliva.
(Live Bait, panel 7074)

Russian

She said gently, ‘What exactly did he say?’
‘That’s the point. I don’t know. He was a foreigner, and he babbled in foreign.' …
‘Breathe nice and easy. Pump the juice into your arms. What did ’e say, then?’
‘Just kept saying “nyet, nyet”. Pennyfeather heaved, chinned the bar, gasped, ‘I say!’ and lost strength suddenly, banging his chin on the bar as he fell. Sprawled on the mat, rubbing his chin, he stared up at Willie and said, ‘Jesus, that’s what he said, Willie! Nyet. He must have been a Russian, eh? ... It’s just come back to me. I sat with him all one night, you know, and he nearly drove me potty with it. Sorok-dva, sto-odin. Sorok-dva, sto-odin. God, I’m not likely to forget that in a hurry.’
Modesty had not moved, only turned her head, but Tarrant could almost feel the excitement in her. She said, ‘It’s numbers in Russian, isn’t it, Willie?’
‘I think so. I can only manage up to ten in Russian, but dva means two.’
(The Impossible Virgin, chapter 5)

“… You know how you can fool around indefinitely on a boat. After dark I usually spend a few hours with the tape recorder and a Teach Yourself Russian course I’m working on.”
(Dragon's Claw, chapter 2)

Modesty [going though files in the University of Health]: Cyrillic script and not a language I read fast—but the file headings should help.
(Garvin's Travels, panel 5201)

“Colonel Mikhail Golitsyn,” said Willie earnestly, “of the Glavnoye Razvedyvatelnoye Upravlemye, formerly of the Komitet Gosudarstvennoi Bezopasnosti, but if you don’t want us to say anything, Colonel, we won’t.”
Modesty said admiringly, “I don’t know how you manage to pronounce all that, Willie. Do you practise with tapes?”
(The Night of Morningstar, chapter 14)

Modesty: Hold it, Willie—I heard two guards talking and I’m glad I use Russian language tapes.
(Fraser's Story, panel 9294)

Other languages

'To anybody who might have overheard, her words would have been cryptic, for she used a mixture of argot from French, Arabic and English, but to Willie Garvin the meaning of every sentence was plain.'
(Sabre-tooth, Chapter 5)

Modesty tells Willie: ‘Their headman, Djut, speaks some Urdu and English. We’ll have to get by with that.’
(The Black Pearl, panel 1158)

Modesty said without moving, very coldly. ‘Alex, there are people here.’ She spoke in Swedish.
Salamander Four

Through the glass transom Modesty could hear a soft, sad wailing in a language strange to her.
(The person wailing is from Indonesia, which has supposedly 700 languages. We can't expect Modesty to know all of them.)
The Soo Girl Charity

Willie addresses the tribespeople in Pidgin, with little success.
(The Iron God, panels 3216 seq.)

Soon these belongings included three books and some packets of coarse paper. Lob spoke five languages, and taught them all to her [Modesty]. Each day of every five days they used a different tongue.
(The Xanadu Talisman, chapter 8)

“Breakfast, then I must spend an hour with a language tape. After that I’ll be going along to a rehearsal room to dance for a couple of hours.” … She was still disciplined, thought Danny as he put away his razor. Fluent in six languages, close to fluent in another four, she rarely missed spending an hour a day with a language tape, either brushing up on one she knew or following a course in a new one.
(Dead Man's Handle, chapter 5)

Dr. Tyl had spoken several words to Willie in a language Modesty thought was Czech. He seemed to expect or to hope that something would happen, and when there was no response he went away looking unhappy. Willie recognised him as the man he had been made to believe was Garcia, the man who had brainwashed him. They concluded that the Czech words were triggers, implanted under narco-hypnosis so that simply by uttering them at any time Dr. Tyl could immediately cause Willie Garvin to fall into a state of deep hypnosis.
(Dead Man's Handle, chapter 11)

[Rudi speaks to his brother in the language of their childhoopd—Czech.]
Rudi: No more talk, Klem. She's not going to back down. We'll beat her up, make it look like a mugging.
Modesty (thinks): Don't know the language, but he's taking off his skis. They're set on stopping me.
(Children of Lucifer, panel 9673.)

[In Tibet]
Willie: The locals are friendly—it’s been useful ’aving a bit of the lingo from last time [referring to The Black Pearl].
…
[A surly question in Chinese and Modesty responds with a few words in Tibetan.]
Modesty: I go … to see father. (The Death Symbol, panels 9798 and 9800.)

English

His [Willie's] speech is Bethnal Green--though I believe his French and Arabic are very good.
(Modesty Blaise, Chapter 1)