The film has attracted attention for its s** scenes as well as the acclaimed performances of actresses Adele Exarchopoulos and Lea Seydoux.
Hollywood veteran Bruce Dern won best actor for his performance in Nebraska.
French star Berenice Bejo, known for silent film The Artist, won best actress for her role in The Past.
The winners were picked from the 20 films in competition and were named at the festival’s closing ceremony on Sunday.
Blue is the Warmest Colour is a three-hour coming-of-age movie in which Adele Exarchopoulos plays a 15-year-old who falls in love with an older woman, played by Lea Seydoux.
Directed by Abdellatif Kechiche, the film won rave reviews in Cannes, being described as “epic yet intimate” by The Guardian.
The film also shocked some critics. The Hollywood Reporter said the “sprawling drama” would “raise eyebrows” as it crossed the barrier “between performance and the real deal”.
Some had questioned whether the s** scenes may make it too e**licit for the top prize.
But director Steven Spielberg, who chaired the jury, told reporters: “I think it will get a lot of play… I think this film carries a very strong message, a very positive message.”
In an unusual move, Steven Spielberg awarded the prize to the two lead actresses as well as the director.
Accepting the prize, Abdellatif Kechiche said: “I should like to dedicate this film to the wonderful youth of France whom I met during the long period while making this film.
“Those young people taught me a lot about the spirit of freedom and living together.”
Blue is the Warmest Colour prevented US film-makers the Coen brothers from repeating their Palme d’Or success of 1991, when they won for Barton Fink.
Their latest film Inside Llewyn Davis, about the 1960s New York folk scene, won this year’s Grand Prix, effectively the runners-up prize.
The best actor award marks a return to the critical bosom for Bruce Dern, who is best known for roles in 1970s films including Coming Home, The Cowboys and The Great Gatsby.
Now 76, Bruce dern has won for playing an ageing, alcoholic father on a road trip to collect a lottery prize. The film, titled Nebraska, was directed by Sideways and The Descendants film-maker Alexander Payne.
Berenice Bejo’s best actress prize has proved that her performance in The Artist was not a one-off. Her film The Past is a family drama made by Iranian director Asghar Farhadi as the follow-up to his Oscar-nominated 2011 drama A Separation.
Mexico’s Amat Escalante, who made brutal drama Heli about the country’s drugs war, was something of a surprise choice for best director.
China’s Jia Zhangke won best screenplay for A Touch of Sin, an examination of rampant corruption in his country.
The Jury Prize went to Like Father, Like Son, about two families who discover that their six-year-old boys were switched at birth, directed by Japan’s Hirokazu Kore-eda.
Films that missed out included Behind the Candelabra, in which Michael Douglas plays the legendarily flamboyant entertainer Liberace, and Italian director Paolo Sorrentino’s The Great Beauty, a sumptuous story about an ageing novelist.
Steven Spielberg was joined on the jury by Life of Pi director Ang Lee, actress Nicole Kidman and Oscar-winner Christoph Waltz.
The other judges were We Need To Talk About Kevin film-maker Lynne Ramsay, French actor Daniel Auteuil, Romanian director Cristian Mungiu, Japanese director Naomi Kawase and Bollywood star Vidya Balan.
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