The festival's prestigious top prize went to a courtroom drama set in the French Alps. German actress Sandra Hüller stars as a writer trying to prove herself innocent of her husband's death.
"Anatomy of a Fall" is the third film directed by a woman to win the Palme d'Or. One of the two previous winners, Julia Ducournau, was part of this year's jury.
Jonathan Glazer takes home second place
The Cannes Grand Prix, the festival's second prize, went to Jonathan Glazer's "The Zone of Interest," a Martin Amis film adaptation about a German family living next door to the Auschwitz concentration camp.
The prizes were presented by a jury chaired by two-time Palm winner Ruben Östlund. The Swedish director won the award last year for "The Triangle of Sadness". The ceremony was preceded by the festival's closing film, the Pixar animation "Elemental".
"Overall, it was a good collection of films this year. I will follow all the winners when they go out into the world, it will be exciting, says Östlund during a press conference after the ceremony, according to AP.
Jury Prize
The jury prize went to Finnish director Aki Kaurismäki's "Fallen Leaves", a love story about a romance that blossoms into a loveless everyday life where reports from the war in Ukraine are regularly played on the radio.
Best Actor went to Japanese film veteran Koji Yakusho, who plays a reflective, middle-aged man in Tokyo who cleans toilets in Wim Wenders' "Perfect Days."