Coppola, 35, is the director of this year's "Marie Antoinette" and was nominated for a directing Oscar for 2003's "Lost in Translation." She won the screenwriting Oscar that year instead.
Mars, 30, is frontman for the French underground band Phoenix, whose biggest hit, "Too Young" from the 2000 album " United," was featured in "Lost In Translation."
Coppola is the daughter of Oscar-winning director Francis Ford Coppola. She played Mary Corleone in his 1990 movie, "The Godfather: Part III."
Coppola wrote and directed the movie "Marie Antoinette." It stars Kirsten Dunst as the 18th-century French queen as well as Coppola's cousin, Jason Schwartzman, who played Louis XVI.
Coppola was married to director Spike Jonze for four years; she filed for divorce in 2003. This is her first child.