"Ça va?" says the young actor to the wise, older director as he passes.

He smiles with twinkly eyes.

"You slept well?" she asks.

"Like a baby," he says. And on he walks.

"Ah, the master," she says.

You wouldn't think these two were at the heart of this year's biggest cinema controversies. Adèle Exarchopoulos is 19, and recently made Blue Is The Warmest Colour, directed by French-Tunisian auteur Abdellatif Kechiche. The film is a three-hour love story between two young women in which very little happens. It is compelling, often brilliant, and contains two astonishingly naturalistic performances from Exarchopoulos and Léa Seydoux.

The jury at this year's Cannes film festival, chaired by Steven Spielberg, awarded Blue Is The Warmest Colour the prestigious Palme d'Or for best film. And, for the first time, the jury ruled that the two central performances were so remarkable that the director should share the award with his actors. There followed giddy photos of the trio celebrating an unprecedented triumph.

And then things took a strange turn. The actors gave interviews in which they talked about Kechiche's tortuous process: how every scene had taken for ever, and how he had insisted on take after take until they felt they were cracking up. They said an explicit sex scene had taken 10 days and that they had to lie on the bed fumbling with each other, cold and naked, hour after hour. "Most people don't even dare to ask the things that he did, and they're more respectful," Exarchopoulos told the Daily Beast. Seydoux said that at times she felt "like a prostitute". A heartbreaking separation and reunion was shot and reshot until they felt battered and delusional. Exarchopoulos complained that the director had made Seydoux hit her repeatedly across the face in a fight scene. No wonder she cries so convincingly.

Then the director fired back. He said the actors were spoiled, didn't know what real suffering was, that he felt "humiliated" and that he didn't want the film released because the audience would no longer be able to watch it objectively.

Yet here we are, a few weeks before the film is to be released, with Exarchopoulos promoting the film in one room, Kechiche in another, and the two engaged in a seemingly warm if brief exchange.

Exarchopoulos tucks into a huge bacon and chicken club sandwich, french fries and tomato and mozzarella salad, and tells me how lucky she has been to work with Kechiche. "I love Abdellatif's cinema. I love his movie. I love the fact that he starts from an ordinary story. I love that he's tried to be close to the truth. I love the humanity in his movie and the power he gave to women in this film."

Exarchopoulos's character is called Adèle, and she is in every scene; in France the film is called The Life Of Adèle, Chapters 1 & 2. Her range is immense, from the unguarded ecstasies of first love to the tear-drenched, snot-dribbling grief of loss. Every scene is so slow and organic that it feels as if you are watching the relationship unfold in real time.

When all three won the Palme d'Or, she says, they were delirious. "I spoke to Spielberg afterwards, and they said they chose to make an exception and give the actors the joint Palme d'Or for the first time. I was surprised we won. We were telling ourselves he's too puritanical, he's not going to like the movie, and in fact he loved it."

I'm confused. They had a wonderful time at Cannes, were widely feted, and everything seems hunky dory today. So was the row exaggerated for publicity?

"No, it was real, but it was not as big as it looks. For me, a shoot is a human adventure, and in every adventure you have some conflict. It is hard when you are young to be pushed to your limits, but for me it was the best school."

Was she misquoted as saying she felt exploited? She nods and shakes her head simultaneously. "No, it's more complicated."

Tell me. "The most important things are too private for me. In every shoot, between the actor and the director there is manipulation. I'm not saying that negatively. It's healthy. Abdellatif records a lot of takes so that you can let go." She says he wants his actors to be in a "second state", instinctive, holding nothing back. "It's extreme, and sometimes it was really hard and he didn't realise it because he has such passion for cinema, for reality, and sometimes it's devouring." She stops. "For me, every genius has their own complexity. And Abdellatif asks you to give him everything. You can trust him like a spiritual father. He will teach you anything, but yes, it was very hard."

Exarchopoulos, whose grandfather is Greek, was born in Paris; her father was a guitar teacher and her mother a nurse. At eight, she joined a dramatic improvisation class. At 12, a director came to watch her and she was cast in a short film. She had bit parts in a number of films, but this is her first major role. She gave up on her baccalaureate to make the film. She says she hated school; not the idea of learning, just the strictures, the mechanical nature of teaching. Was she academic? "No, I was mediocre. The less I did, the better I felt. I was lazy. I hate having things imposed on me. I hate it when people impose a certain rhythm."

Exarchopoulos couldn't be more French: her looks, her smoking, her emotional transparency. She has a lovely round face yet to lose its puppy fat, a sensual innocence that reminds me of a young Charlotte Gainsbourg, and a refreshingly belligerent intelligence. When bored by a question, she'll look out of the window. When interested, she gives it her all.

I ask Exarchopoulos to describe Adèle's character in the film. "She's a young girl, a virgin of all experience in life, and she's got a crush on somebody, and it is her first love. She is pure. She doesn't know the rules of love, like you have to protect yourself. She wants to give everything. I was the same with my first love. I give everything, I want to believe everything, I want to live everything, eat everything." How old was she? "Fourteen."

I tell her that even middle-aged people don't know to hold things back, to protect themselves. "They should know," she says incisively. "They will learn." It makes me smile.

Would she say she was unusually mature for her age? "Maybe, I don't know. It depends on your experiences. For example, I've always spent time with older people, and that helps." At one point, she tells me that Kechiche, 52, was easy prey for journalists because he is naive.

Blue Is The Warmest Colour is superb on class (Adèle's parents are working class, her lover bohemian middle class); snobbery (her lover belongs to a patronising art elite); bullying (her fellow pupils pick on Adèle when they think she is having an affair with a woman); school (Adèle becomes a teacher, and the film has some of the most tender scenes you will see with young children); and, as you might expect from the man who directed Couscous, food (Adèle eats plate after plate of pasta, splattering it all over her face; her lover's family prefer oysters).

Every scene is languorous, as if the director has created a reality for his actors, and then filmed it over five months. For me, the one weakness is the extended central sex scene, when the film briefly descends into Confessions Of An Auteur, with lots of bottom-slapping and pinching. I tell Exarchopoulos I think it's too long, and that it looks like a man's projection of lesbianism. "I think you can't really judge sexuality. Sometimes, you see people in life and you can't imagine, 'Oh, she's going to have sex.' But I do agree that they are too long."

What about all the slapping? "Everybody gets slapped in sex," she says matter-of-factly. "It's a kind of highway to sex."

Adèle's two most powerful scenes are when she breaks up with her lover, and when she attempts a reconciliation. I have never seen an actor weep with such raw intensity. When she talks about the way Kechiche manipulated her, I think of these scenes. Surely she couldn't have broken down so completely unless he had driven her to the edge with retake after retake? Is this what she found so painful?

"You can't summarise a five-month experience around a hamburger. It is too intimate. These are things you don't discuss. It's just sometimes you were destabilised by the fact that he was pushing you to your limits. But that's what we loved, too. He's waiting for the greatest moment, and he would always take the best from you."

Does part of her emotion come from the exhaustion? "Yes, for sure. Yes, you lose yourself."

I ask if making the film has given her more confidence. "No. Because everyone has tried to judge me, to put something on my shoulders. Some people want me to be a gay militant. I have hate messages on Facebook, racist or homophobic: they talk about an Arabic man making two girls have sex. Then some people say,  'Will she be good in the next film or is it just Abdellatif Kechiche?' I'm only 19. Stop asking me what I'm going to do tomorrow. I don't know."

She throws back a couple of chips, takes another bite out of her sandwich and says that, despite everything, "This is the best thing I have ever done in my life."

Great, I say, so we'll set the record straight and say that you will work with Kechiche again. "I don't know. I have to prove myself with somebody else also. I was 18, I was suffering on this movie, nobody can understand because nobody was there. Maybe in two years' time, I will say yes." If he asked her now? "I will say I don't know. Please give me time to live my life, to discover myself, to work with other people, to learn."

If Kechiche had gone ahead with his threats not to release the film because he was so hurt by his stars' comments, would she have been upset? She deadpans, and tells me it's a daft question, because it is coming out.

Yes, I say, but what if he had withdrawn it?

She laughs. "What d'you think? I gave myself for five months, everything I can."

I think you would have been devastated, I say.

"Yes, of course."

• Blue Is the Warmest Colour goes on limited release on 22 November