At age 16, Aumont began studying drama at the Paris Conservatory, where his mother also studied. His professional stage debut occurred at the age of 19. His film debut came one year later when Jean de la Lune (Jean of the Moon) was produced in 1931.

However, his most important, career-defining role came in 1934 when Jean Cocteau's play La Machine infernale (The Infernal Machine), was staged. While his film and stage career began rising quickly, World War II began. Aumont remained in France until 1942 when he realized that as a Jew he would have to flee the Nazis. He migrated from the unoccupied zone of Vichy France to New York City, then to Hollywood, California to pursue his film career. He began working for MGM, but after finishing The Cross of Lorraine, he joined the Free French Forces. He was sent to North Africa, where he participated in Operation Torch in Tunisia. He then moved with the Allied armies through Italy and France. He was wounded twice. The first was on a mission with his brother; the second was more serious. Aumont's Jeep was blown up near a land-mined bridge. General Diego Brosset, commander of the 1st Free French Division, to whom Aumont was aide de camp, was killed.[citation needed] For his bravery during the fighting, Aumont received the Légion d'Honneur and the Croix de Guerre.[1]

After the war, Aumont quickly resumed his movie career, starring with Ginger Rogers in Heartbeat (1946) and as the magician in Lili (1953) with Leslie Caron. He worked with a number of prominent theatre director and stars, including his (then) wife Maria Montez. In the mid-1950s, Aumont began working in television, appearing on several anthology programs, such as Robert Montgomery Presents and as a guest on the show What's My Line?. In the 1960s and 1970s, he appeared in various theater productions, including the musicals Tovarich with Vivien Leigh, Jacques Brel Is Alive and Well and Living in Paris, South Pacific, and Gigi.

One of his later performances was in A Tale of Two Cities (1989). Two years later, in 1991, aged 80, he received an honorary César Award as well as being decorated with the cross of Commandeur des Arts et des Lettres.[2]