The laws of journalism maths dictate that young + beautiful + French = ingénue. Léa Seydoux, the 31-year-old Parisian actress, has been called one in print at least 34,000 times. However, a rainy afternoon with her in a café on the edge of the Parc de Buttes-Chaumont demonstrates that she is no innocent. Seydoux is as unsophisticated as a diplomat, as guileless as a wolf. She is the kind of person who, tiring of her fear of flying, marches herself up to the ticket counter and buys a ticket for the shortest flight leaving that day. (She ended up in Lyon.) "When I was young, I was so scared about death," she says. "It was like I was in a kind of depression. I didn't know if life was worth living, and now I think that yes, it is." All this before having taken a sip of her chocolat chaud.

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Sweater by Louis Vuitton.Jewellery by Charlotte Chesnais

Ask about her siblings, however, and she grabs your phone to fire up Instagram and starts surfing her sister's feed. Then she gets her own phone and pulls up pictures of the monogrammed pillows from her family's African cooperative that she made for Marion Cotillard — her co-star in It's Only the End of the World, directed by Xavier Dolan — and Cotillard's family. Seydoux's perfect, chatty English is the legacy of six summers at Camp Timber Ridge on the East Coast. ("You know the marshmallow with the chocolate? And the rice with the marshmallow?") Her favourite word in English is overwhelming.

We think of the actress, per her archetype, as a fresh and simple soul, the girl from the provinces drinking Champagne for the first time. But everything about Seydoux — christened Léa Hélène Seydoux-Fornier de Clausonne and once described as "Bardot plus Binoche plus Kate Moss and sometimes all three at once" — is mature. She's old world, old money, old-fashioned. (No wonder Woody Allen, who cast her in 2011's Midnight in Paris as an antique dealer, has a thing for her.) Her grandfather is the chairman of the venerable French film company Pathé; her father founded the technology company Parrot; and her mother lives part-time in Senegal, where she runs a fair-trade charity. They are pillars of the French establishment, the sort of people who invite Chiracs and Lévys and Louboutins to their weddings.

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But what Seydoux's childhood offered in privilege, she says, it lacked in structure. Her parents split up when she was three, and she's spoken of a solitary and melancholic childhood that didn't have enough rules. She first sought the help of a psychologist at the age of 14. When she realised, several years later, that she wanted to become an actor, her family's stature seemed less like a free ticket than an extra piece of baggage. "In France, it's hard to become someone on your own," she says. "Even if you're a superstar, they will always say, 'Yeah, but you come from that world.' It's difficult to have ambition if you live in Paris."

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Good thing, then, that she is finding an audience outside France. You may remember her performance — if you saw it, you will definitely remember it — in Abdellatif Kechiche's Blue Is the Warmest Colour (2013), for which she was awarded the Palme d'Or. You may also remember how, at the height of the film's triumph, she publicly slammed Kechiche, saying that the filming had made her feel like a "prostitute" and that she'd never work with him again. "I think that I was angry and that I had to express my anger," Seydoux says. "I really wanted to do it, because I love his work, but I knew this was the price to pay. Maybe I felt strong because of the film and the success of the film made me strong. Everyone was like, 'Kechiche, Kechiche, Kechiche,' and I just wanted to say, 'OK, he's not, like, untouchable.' I wanted to say the truth, not for him but for me. I had a need. It's not something that I regret."

She loves working in America, where she "feels the pressure less". But American men? "Yeah, of course, why not?" she says initially, pondering whether she could ever fall in love with one. "But I don't find them very… there is something not so sexy about American men. They are too self-conscious and they spend too much time at the gym." Yeah, not an ingénue.

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Swimsuit by Y-Project. Trousers by Pallas Paris. Jewellery by Charlotte Chesnais

Styling: Niki Pauls