He emigrated to Paris in 1933, after studying five years in Berlin. There he met Jacques Prévert, with whom he wrote around 80 songs. Kosma met Marcel Carné through Prévert and during the Occupation of France (World War II) he worked for him.
He is probably most known for the song "Les feuilles mortes" ("Autumn Leaves"). The piece was originally meant for an opera, but Kosma and Prevért convinced Carné to turn into a film: "Les portes de la nuit" (1946). The lyrics were originally written by Prévert, the English lyrics were written by Johnny Mercer.
After the war, Kosma wrote scores to numerous films, and he continued writing music for films until his death. In his last years, he also composed two operas "Les Hussards" and "Les Canuts".
Related to conductor Georg Solti.
He died on August 7, 1969 in La Roche-Guyon, France.