Back in 2005, studying in Montpellier, in south-eastern France, Tahar Rahim found himself the subject of a documentary named Tahar the Student. In one scene, we see him in his bedroom, with a poster on the wall for Al Pacino in Scarface; four years on, the young French actor would be widely compared to Pacino in that very film.

Rahim had only appeared in one feature, a bit part in a horror movie, before his explosive breakthrough in Jacques Audiard's 2009 thriller A Prophet. He played Malik, a gauche young petty criminal who rises through the ranks of prison society to become a ruthless gangster, and the performance – quiet but assured, and compellingly feral – won Rahim two of France's prestigious César awards, for best actor and brightest male hope. But it was anyone's guess then whether he had an illustrious future ahead of him or whether he would join the over-populated ranks of cinema's inspired one-offs.

Five years on, it's clear that Tahar Rahim is here for the long haul, and a lot of students around the world now decorate their walls with posters of A Prophet. Rahim has appeared in another 10 features (he's currently shooting the 11th), and, while they're not all in the league of A Prophet, they largely feature him in roles chosen with seriousness and executed with tough grace.

The latest is The Past, an intense Parisian drama by Asghar Farhadi, the Iranian director of A Separation, with Rahim as the third corner of an emotional triangle that also contains Bérénice Bejo, from The Artist. Rahim's character – Samir, a drycleaner with tragic family troubles – is a sullen, taciturn figure, the actor's restraint throughout bringing a stable centre to a film that's otherwise prone to hair-tearing histrionics. Samir resembles him the least of all his characters, Rahim tells me: "He doesn't move much – I can't stay still for a moment."

Sure enough, when I meet him in a café near Paris's Place de la République, Rahim is quite the live wire. Lightly bearded, he bounds in, grinning, in a boho-chic ensemble of leather jacket, designer shades and flat cap, which he takes off to reveal an artfully jagged short haircut. He's hyper-alert, looks you straight in the eye while talking, and his conversation in French speeds up heatedly, punctuated by expansive hand signals, when he gets onto a subject close to his heart, such as his favourite Korean directors or the American cinema of the 70s – "A cultural renaissance! Boom! A total explosion!"

Films such as The Past, he says, are "the kind I most like watching – the kind that make you think about the human condition. I like films to be pure cinema, but I also like them to provide a snapshot of a family, a society or a character – something that can nourish you as a human being as well as an actor."

Farhadi's directing style, Rahim tells me, is all about absolute precision and extremely detailed rehearsal, down to the last gesture. Rahim was worried that this approach would inhibit him, but he found it strangely liberating. "It almost becomes like bunraku – Japanese puppet theatre – on a human scale. It's worked out to the millimetre. It taught me to work differently, with constraints, and I loved it."

Now 32, Rahim grew up in Belfort in north-eastern France, the youngest of 10 siblings (the oldest more than 20 years his senior); they were raised by their Algerian mother, whom in Tahar the Student he calls "la femme de ma vie". He won't talk about his father, though, or discuss his family background. "When you do this job, you give everything to the public – your emotions, your private self, your body, your face. There are places I keep for myself," he says, putting a hand on his heart, "and family is one of them."

As a boy, his cinephilia was encouraged by two of his brothers and by a man known as Mentor who ran a private video club on the 13th floor of the family's tower block, renting out a bootleg collection of 500 titles. Rahim knew in his early teens that he wanted to act, but decided to study film first in Montpellier. "I knew I'd have to go to Paris eventually and I didn't want to be the provincial kid who just turns up and says 'I want to act'." He didn't only study acting, he says, but "film history, lighting, production, the whole business. It all helped."

Signing up for work as an extra brought Rahim into contact with a director who decided to make him the subject of a documentary – or rather, "a documentary fiction, a hybrid". Tahar the Student cheats with some of the facts, he admits, putting a conspiratorial finger to his nose, but it's basically true to his life then. He hasn't seen it since it was made. "I'd rather watch it later because, for me, it's not just a film, it's a piece of memory." Rahim's first acting break was in the 2007 TV series La Commune, scripted by Abdel Raouf Dafri, one of the writers of A Prophet. It was about crime and cultural conflict on a housing estate; Rahim's character was "a small-time hood with dreams of power, who's a bit disturbed. If there had been a second series, I think he'd have become absolute evil."

A Prophet came out two years later, and was immediately acclaimed not only as a superb thriller but as a cultural turning point. Its gangster anti-hero and realistic underworld background broke with the derogatory, cartoonish or earnestly affirmative representations of Arab characters that had long prevailed in French cinema. As the newspaper Libération put it, "having a 50% Arab cast in a genre movie … is a powerful gesture, more powerful than any anti-racist tract or screenplay".

The film, Rahim agrees, "pinpointed a real problem in French cinema, to do with the representation of minorities. It really changed things. But I don't like the term 'minorities', it stigmatises." He makes a point of avoiding stereotypical roles: "I've always refused to play terrorists. If it helps change things, OK – but not if it maintains the status quo of what appears in the media."

After A Prophet, he played two out-and-out Arab heroes – a black-marketeer turned French resistance fighter in the wartime drama Free Men, and in Black Gold, set in a fictional Gulf state that suddenly strikes oil, the studious son of a sheikh who becomes a glamorous desert warrior. A touch of romantic cliché there, surely? "I imagined it would go a little deeper," Rahim concedes.

He is wary of expectations that he should be a role model for France's Maghrebi communities. "I don't get into all that. I'm not here to carry a flag and say I represent this or that. Other people do it really well. I'm an actor, full stop. Not an Arab actor. Not an actor of Algerian origin. Just an actor."

I ask whether he felt uncomfortable when reviews of A Prophet hailed him as a new Pacino. He grins and rubs his fingers together briskly, a gesture I don't quite follow. What does it mean? "It means fear! Pressure! It terrified me." The key thing, he says, is to keep some distance. "Acting isn't an obsession for me – and it mustn't be an obsession, it should be just a job."

It's certainly a full-time job: 10 completed features since 2009. Some have inclined more to the mainstream, like the forthcoming The Informant, a rather functional true-crimer about drug smuggling in Gibraltar; or the comedy he's currently shooting, about a burglar whom a small boy mistakes for Santa Claus. Strangest of all was the Celts-and-centurions swashbuckler The Eagle, for British director Kevin Macdonald. Rahim played the Seal Prince – shaven-headed, covered from head to foot in loam, and speaking ancient Gaelic.

Then there are a series of more intense art films – such as Love and Bruises, a tale of Parisian amour fou. That wasn't an easy experience – partly because the Chinese director Lou Ye had to communicate through an interpreter (and then not very much: "Zero direction," Rahim shrugs), partly because of the intimacy involved. "If it's sexual, that worries me. Emotional I don't mind, sexual I can't handle. I nearly didn't do it because of the nude scenes. It was agony."

Differently agonising was Our Children (2012), a superb but harrowing drama about a couple (he's Moroccan, she's Belgian) undergoing extreme meltdown brought on partly by cultural difference. Rahim rolls his eyes. "Phew! It was tough. But I keep a distance from my characters. I'm not one of those actors who becomes another person to make a film, and I'm not sure they exist anyway. I work in the moment – when I'm there I believe in it, and when I go home, I'm me."

It's only five years since A Prophet transformed Rahim's life – for one thing, he is now married to Leïla Bekhti, another rising French star, who acted with him in that film. But his marriage is another subject he declines to discuss. "Don't take it personally!" he says in English, grinning and putting his hand on my wrist to signify no hard feelings.

Despite his guardedness, Rahim perhaps reveals more than he intends when he talks about the effects of success. "People look at you differently. Sometimes they take out their frustrations. It comes out in little details – you get shouted at a lot more for no reason, and you have to give people time to cool down. Because it can come as a shock to someone you've grown up with – boom! you explode, suddenly you don't belong just to them but to everyone, and they think they're losing you. It can be hard to deal with."

You can see how the people around Rahim might find his new life so startling, and why he might find it all hard to balance. For his forthcoming film, The Cut, by acclaimed German director Fatih Akin, he went on an exhausting shoot that took in six countries including Canada, Cuba, Jordan and Germany; not the least of the challenges was dealing with the extreme changes in climate. But that's what excites him, he says, the cosmopolitanism of it all. "Working with an Iranian, a Belgian, a Chinese, a Frenchman, a German Turk – that's what I like in cinema, travelling. New, fresh cinema – that's what I want to do."

What about time to …, I start to ask, but Rahim cuts me off. "To breathe? I don't really think about that. I'm not ready to stop and look back yet."