Jury president Steven Spielberg said the coming-of-age tale about a 15-year-old French girl’s first love, an older woman, had been a unanimous choice.
Tunis-born Kechiche dedicated the prize to the youth of France, and the revolutionaries of the Arab Spring.
“They also have this aspiration to live free, to express themselves freely and to love in full freedom,” he said, adding later that he hoped the film would also be distributed in socially conservative Tunisia.
The runner-up award, the Grand Prix, went to Joel and Ethan Coen’s Inside Llewyn Davis starring Carey Mulligan, Justin Timberlake and Oscar Isaac in the title role of a luckless folk singer in 1960s New York.
The Coens’ Barton Fink won at Cannes in 1991 and they were in the running in 2007 with No Country for Old Men.
Mexico’s Amat Escalante claimed best director for the ultra-violent Heli about his country’s blood-drenched drug wars.
French actress Berenice Bejo won the best actress prize as a Parisian mother in Oscar winner Asghar Farhadi’s family drama, The Past.