She will play Vesper Lynd in the forthcoming movie, starring Daniel Craig as 007.
The 25-year-old made her first big screen film, The Dreamers, three years ago, about an incestuous brother and sister who befriend a young American during the Paris student riots of the 1960s.
She made her first Hollywood film last year when she appeared with Orlando Bloom in Ridley Scott’s historical drama Kingdom of Heaven.
The Dreamers’ director Bernardo Bertolucci once said of the actress: “She’s so beautiful it’s indecent.”
It has also been announced that Danish-born actor Mads Mikkelsen, 40, will play Bond’s nemesis Le Chiffre, and US star Jeffrey Wright, 40, has joined the cast as Felix Leiter.
Mikkelsen made his American debut opposite Clive Owen and Keira Knightley in Disney’s King Arthur.
Wright has appeared in films such as Shaft, Ali, The Manchurian Candidate, Broken Flowers, and Syriana.
Casino Royale will be the 21st James Bond film and is based on Ian Fleming’s first Bond novel.
It is directed by Martin Campbell, who was previously at the helm of 1995 blockbuster GoldenEye.
The movie will be released worldwide on November 17 and will be filmed on location in the Czech Republic, the Bahamas, Italy and Britain.
Bond producers Michael Wilson and Barbara Broccoli said: “After an extensive search we have found the perfect actress.
“Eva is one of France’s most accomplished young actresses, now receiving international acclaim.
“She brings to the complex role of Vesper an exciting combination of enigmatic and seductive beauty.”
Amy Pascal, chairman of the Columbia Pictures Motion Picture Group, said: “Vesper is a pivotal role in Casino Royale and it takes much more than beauty to make this role work.
“When you think about the great James Bond adventures, of course you think about action and espionage, but you need to have palpable sexual tension in the movie and in casting Vesper, we really needed to up the ante, because this character is very much an equal to Bond and central to our story.”