In a hotel suite in Paris, Marion Cotillard is behaving like a monster. We are about to start our interview when her three-year-old sprints in with his nanny, and before I have a chance to ask my first question, Cotillard has leapt on all fours and is skidding across the carpet letting out strangled roars. There’s a chase in which she plays Godzilla (upright, with claws), and Marcel, her son with French actor and director Guillaume Canet, squeals with delight. Finally she resumes her position on the sofa with Marcel still chuckling impishly under one arm. “He’ll get bored soon,” she reassures me.

Cross-legged and clad in tweed hot pants, she looks like a particularly soignée teenaged mother: her face has never lost its adolescent curves and her body barely looks 20 years old (she’s in fact 38). When Cotillard bent herself into the prematurely aged Edith Piaf in La Vie En Rose, a morphine-addicted, cancer-ridden husk of a woman, Trevor Nunn called it “one of the greatest performances on film ever”. Meeting her, you appreciate why.

In the seven years since winning the Best Actress Oscar for her role, Cotillard has shown herself to be consistently drawn to complex, tortured women. Her recent work, if less transformative, has been just as unflinching: a double-leg amputee in visceral love story Rust and Bone; a young Polish refugee in New York manipulated into prostitution in The Immigrant. In her latest film Two Days, One Night by Belgian auteurs the Dardenne brothers, she plays Sandra, a factory worker who, after a period of sick leave due to depression, is forced to petition her colleagues to vote for her in a work ballot. They’re faced with a cruel moral dilemma: her job or their annual bonus. It’s a raw, empathic portrait of mental illness.

She seems to relate to outsiders, I say. “I’ve always felt an outcast,” Cotillard replies. “There is something strange about me. I don’t ever feel at ease in a group of people. I have to fight hard to overcome my fears.” What are these fears? She smiles. Her eyes are alert, glassy, and look as if they could brim with tears at any moment. I’m left to find meaning in her gaze. It’s all very Mona Lisa.

It is this mysterious quality that seems to appeal to directors, from La Vie En Rose’s Olivier Dahan (who wrote the screenplay with Cotillard in mind because he saw something tragic in her eyes) to an imposing list of American filmmakers: Christopher Nolan (Inception and The Dark Knight Rises), Michael Mann (Public Enemies) and Woody Allen (Midnight in Paris). Today she is one of the highest paid non-American actresses in Hollywood, although she has never turned her back on low-budget French-language film. For the Dardenne brothers, who have only worked with unknown actors throughout their 40-year-long career, casting Cotillard in Two Days, One Night was a risky move, not just because of the Hollywood baggage but because of her fashion status as one of the faces of Christian Dior. The underdog-loving jury at the Cannes Film Festival has already overlooked Cotillard for the Best Actress prize three years in a row. But this year the Dardennes – three-time Palme d’Or winners – also walked away empty-handed. “For me? I really don’t care,” she says, waving a hand in the air. “But the film? Yes. The Dardennes get an award every time they go to Cannes, so I got a little paranoid and thought: ‘Oh my God, maybe it’s my fault.’”

Cotillard is a fanatical researcher, so when I ask how she constructed her performance I’m expecting a tale about observing patients in Belgian institutions. “The preparation was very light this time,” she says, shifting into a half-lotus position. “Medical information on panic attacks and the side-effects of Xanax. I understand depression. I was never super-depressed, but at one point I thought it was coming.” At this point she dispatches Marcel, fidgety and bored, to his nanny. “I’ve had many turning points in my life like that. I’m able to tell when I’m in a bad place or super-sad and move on. When you’re stuck somewhere you need to change something, to shift the energy.”

One such time came after filming La Vie En Rose, when Cotillard had let herself be swallowed up by Piaf, shaving her eyebrows and hairline, willing her body to shrink nine inches (Piaf was 4ft 11in) and sitting for five hours a day in make-up. It was less of a performance, more a demonic possession. After the shoot wrapped, Cotillard says she continued to be haunted by Piaf, sometimes speaking in her gravelly voice. Piaf stayed with her for a total of eight months. “I tried everything,” Cotillard tells me. “I did exorcisms with salt and fire. I travelled to Bora Bora to escape her. I went to Peru to Machu Picchu and did ancient shamanic ceremonies to cleanse myself after I eventually realised why I couldn’t let her go. She had been abandoned as a child. Her greatest fear was to be alone.”

Now that she has Marcel, she says she is unwilling to plunge so deeply into a role, to lose herself in what she calls the “total darkness”. She recently filmed Justin Kurzel’s new adaptation of Macbeth, playing Lady Macbeth opposite Michael Fassbender. “Before my family, everything in my life was dedicated to the character. The more deeply affected I was by her, the closer I felt to her. But I cannot lock myself away in another world any more. I don’t want it to affect my son when I’m in a weird state because I’m ‘depressed’ or ‘killing a king’.”

Cotillard says she’s always been “sensitive”. As a child she was a shy, melancholic loner riddled with very early-onset teenage angst. “I had existential dilemmas as young as seven, obsessive questions about my place in the world. Where did we come from? Why am I here?” She grew up in Alfortville, a suburb of Paris to French “bobo” parents – bourgeois bohemians. Her mother Monique Theillaud was a mid-level theatre actress, her father Jean-Claude Cotillard a Breton mime artist and theatre director. Together with Cotillard’s younger identical twin brothers, Guillaume and Quentin (a writer and a sculptor), they lived in a flat on the 18th floor of a tower block where they were allowed to draw freely on the walls. But excluded by her brothers’ symbiotic relationship, Cotillard didn’t talk much: “I couldn’t identify with anyone. At school I was considered very strange. I didn’t understand the relationships between people.”

From an early age she was drawn to imaginary stories. When she saw ET, aged seven, she was so distraught she had to be removed from the cinema. Her father also introduced her to silent films. “I used to pretend I was Louise Brooks or Greta Garbo in my bedroom,” she says mimicking her younger self. “I absorbed a lot from my father. He taught us how to mime at home with games.” When he set up his own theatre company, the family moved to La Beauce, near Orléans. Theillaud began teaching at the Conservatoire d’Art Dramatique d’Orléans, where the teenage Cotillard enrolled to study acting. “I saw it as a way to escape myself,” she tells me. “But it was through acting that I met myself.” On graduation she moved to a rundown flat near Gare du Nord station and appeared in the TV series of Highlander at 18, after which she was never unemployed.

In 1998 Cotillard got her first big film break in Luc Besson’s Taxi. She met Canet, then married to Diane Kruger, on the set of Love Me If You Dare six years later, and the friends reconnected after Canet’s divorce from Kruger in 2006. In France the couple are equivalent to Brangelina, but photographs of Cotillard with Canet in public together are rare. Little is known about their life together, although they both separately admit to being guitar geeks (their flat in the Marais is crammed with various models, and until recently Cotillard played bass for Parisian singer Yodelice as her butch alter-ego Simone). Cotillard agrees that the country’s strict privacy laws allow them breathing space. “Having your picture taken in the street and put in a magazine won’t change your life. But what happened to people in England, hacking phones. It’s vomit. It’s sick. This fucking changes your life.” She almost retches with disgust. “If someone is cheating on their wife in the street and pictures are taken, fine, that’s their risk. I’m not talking about some people... who currently run this country.”

This, you presume, is a reference to François Hollande’s extramarital dalliance with actor Julie Gayet. Despite appearing to prefer life on the spiritual plane, she is surprisingly engaged with politics, and when I bring up the Front National’s landslide majority at the European elections, she makes a “Quelle horreur!” expression: “French politics is a circus. The French people like to shake things up a bit, but Marine Le Pen getting into government? This will never happen. Never.”

Her real passion, however, is the environment. She’s a locavore (where possible, she eats locally produced food) and has been recycling since the 80s, a habit learned from her Breton grandmother. She’s also an ambassador for Greenpeace: in 2010 she went to the Congo to make a series of films about the destruction of the rainforests by logging companies. The following year she supported Amazonian Indian Chief Raoni in his fight against the construction of the Belo Monte hydroelectric dam in Para, Brazil. Then last year she caged herself, literally, with other demonstrators outside Paris’s Palais Royal in protest over the detainment of the Arctic 30 in Russia. Her current cause is the endangered Sumatran tiger.

“I’m a nature lover, but I’m a human being lover, too. Nature will survive us. The thing we’re going to fuck up is us – and animals,” she says. “Destroying what makes us live is sick. More people are waking up but it’s super-slow. Why don’t we listen to the wise men in our world?” She reels off a list: Al Gore, French-Canadian astrophysicist Hubert Reeves and Algerian writer and farmer Pierre Rabhi. She is aware of the paradox of being both an environmentalist and a frequent long-haul-flying actor, plus the muse of Dior, part of the haute-fashion conglomerate LVMH. This is the one chink in the Cotillard matrix. “Campaigning and acting aren’t compatible,” she admits. “That’s why Audrey Hepburn gave up acting. That’s why Angelina Jolie will give up. I’m not ready to stop yet.”

Still, some things are changing. You get the sense that after Lady Macbeth she is growing a little weary of tragic antiheroines. “The dream,” she says, “is to do comedy.” Her first foray in the genre was a cameo in Anchorman 2 last year. “Comedians I know, like Will Ferrell, Jonah Hill, Jean Dujardin, are some of the best human observers. Comedy has deep insights into our human defects that somehow affect the audience more deeply than tragedy.” She pauses while I absorb this, then she shrieks: “Oh! And I’d like to play a man.”

Inevitably my mind leaps to Hamlet – the ultimate tortured soul. “Oui! C’est ça!” she cries, slapping her leg when I suggest it. “But on the stage in London, unannounced. So no one knows it’s me… I could totally disappear.”

Two Days, One Night is released in cinemas nationwide on 22 August

• Peter Bradshaw’s Cannes review of Two Days, One Night
  
• Watch Marion Cotillard in a deleted scene from Rust and Bone