French director Jacques Audiard's film Dheepan has won the top prize at Cannes, the Palme d'Or.
The gritty drama tells the story of refugees fleeing post-civil war Sri Lanka for a life in France.
The choice made by the jury led by American filmmakers Joel and Ethan Coen was a surprise.
Holocaust drama Son of Saul took the Grand Prix. Vincent Lindon won Best Actor while Rooney Mara and Emmanuelle Bercot shared Best Actress.
Dheepan tells of a former Tamil Tiger fighter who links up with two strangers to pretend to be a family and find a life of asylum in a tough, drug-infested housing estate on the edge of Paris.
Audiard, who previously made A Prophet and Rust and Bone, said: "To receive a prize from the Coen brothers is something pretty exceptional. I'm very touched. I'm thinking of my father."
Joel Coen said: "This isn't a jury of film critics. This is a jury of artists who are looking at the work."
The Grand Prix, essentially the runner-up prize, went to Hungarian newcomer Laszlo Nemes for Son of Saul and its depiction of the Auschwitz, gas chambers.
"This continent is still haunted by this subject," he said.
68th Cannes Film Festival top awards:
Palme D'Or: Dheepan
Grand Prix: Son of Saul
Jury Prize: The Lobster
Best Director: Hou Hsiao-hsien
Best Actor: Vincent Lindon
Best Actress: Rooney Mara and Emmanuelle Bercot
Best Screenplay: Michel Franco (Chronic)
Camera d'Or (Best first feature): La Tierra Y la Sombra
Greek director Yorgos Lanthimos took the jury award, the third prize, for The Lobster, a dystopian comedy starring Colin Farrell and Rachel Weisz.
Best Director went to Taiwan's Hou Hsiao-hsien for martial arts film The Assassin, his first movie in eight years.
Rooney Mara shared Best Actress for her role in Carol, but her co-star Cate Blanchett was overlooked and instead the jury decided to honour Emmanuelle Bercot for her role in My King.
Vincent Lindon's Best Actor award was for his role in Stephane Brize's film The Measure of a Man.
There were 19 in-competition films this year, though several were aired out of competition, including Mad Max: Fury Road and Pixar's Inside Out.
The festival was also overshadowed by a row over footwear.
Several women reported being turned away from screenings for not wearing high heels.
Film producer Valeria Richter, who has part of her left foot amputated, says she was one of those stopped.
The festival denied heels were part of the official dress code.