Marion Cotillard gives birth to a son

(CBS) French actress Marion Cotillard and her actor-director boyfriend, Guillaume Canet, are now parents to a baby boy.

The Oscar-winner gave birth to a son, named Marcel, in Paris on Thursday night, a source told People magazine.

Pictures: Celebrity babies
Pictures: Marion Cotillard

"Mother and baby are fine," the source said, and Cotillard is "very happy."

Canet, 37, and Cotillard, 35, starred together in 2003's "Love Me If You Dare" and began dating in 2007. The pregnancy was first reported in January.

Cotillard won an Academy Award for playing French singer Edith Piaf in 2007's "La Vie En Rose." She'll star alongside Christian Bale, Anne Hathaway and Joseph Gordon-Levitt in Christopher Nolan's upcoming Batman film "The Dark Night Rises, and previously starred in Nolan's "Inception."

She also has a role in Woody Allen's "Midnight in Paris," which opens in New York and Los Angeles on Friday.