Among the 14 films in competition, "Whiplash" was a hit with the public and received the audience prize for favourite film as well.
The drama tells the story of a young drummer at a Manhattan conservatory trying to become the best of his generation under the direction of a hard-nosed teacher.
Chazelle himself had been a drummer in his youth and said he had a difficult time learning the instrument.
He said he wanted to convey the emotions he had felt by making each concert in the film seem as if it were a matter of life or death.
The jury grand prize went to French-Canadian director Philippe Falardeau's "The Good Lie", starring actress Reese Witherspoon, which tells the story of four orphans who survive an attack on their village in South Sudan and 10 years later emigrate to the United States.
A highlight of the 40th edition of the festival — which celebrates American movies — was the biopic of funk music star James Brown, "Get on Up", by director Tate Taylor with Rolling Stones singer Mick Jagger as one of the producers.