She quickly established herself as one of the country's most successful film actresses. After seeing her in the 1934 film Lac Aux Dames (USA title: Ladies' Lake), Darryl F. Zanuck brought her to Hollywood in 1936 with a widespread publicity campaign.

However her films for 20th Century Fox were only moderately successful, and Simon returned, dissatisfied, to France. There she appeared in the film La Bête Humaine (The Human Beast) in 1938.

With the outbreak of World War II she returned to Hollywood and RKO Studios where she achieved her greatest successes in English language cinema with The Devil and Daniel Webster (1941), and the horror films Cat People (1942) and The Curse of the Cat People (1944).

These films, however, did not lead to greater success and she languished in mediocre films until the end of the war.

She returned to France to act, and appeared in La Ronde (1950). Her film roles were few after this and she made her final film appearance in 1973.

She died in Paris, France on 22 February 2005, aged 94 from natural causes. The BBC mistakenly reported her age as 93, by using the wrong year of birth (1911).

She never married but had numerous intimate relationships with fellow actors or musicians, among others. Her maid revealed that she gave a gold key to her boudoir to any man she was interested in, including George Gershwin.