The jury also presented a special prize to Kidman to celebrate the festival's 70th anniversary.
The big winners from this year's Cannes Film Festival have been announced.
German-American Diane Kruger won the best actress prize for her nuanced performance as a Hamburg woman who loses her Turkish husband and six-year-old son in a bomb blast triggered by neo-Nazis in Fatih Akin's "In the Fade".
Coppola's win is an important moment for a festival that has only seen one female filmmaker awarded the Palme d'Or - Cannes' top prize. Kruger dedicated her win to everyone who "has survived an act of terrorism and who is trying to pick up the pieces and go on living after having lost everything". "Merci beaucoup madames et monsieurs!"
Russian director Andrey Zvyagintsev's Loveless, a drama about how society is struggling under Vladimir Putin, took the "Jury Prize", considered third place at Cannes. Sofia Coppola took home the Best Director award for her film 'The Beguiled'. You Were Never Really Here director Lynne Ramsay tied for the Best Screenplay prize, sharing the honor with Yorgos Lanthimos and Efthymis Filippou of The Killing Of A Sacred Deer, which also stars Kidman. "Thank you a thousand times", she said.More news: Israel's Cabinet meets in Western Wall tunnels, approves Old City elevator
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Joaquin Phoenix with his best actor award for You Were Never Really Here.
Taking to the stage of the Palais de Festivals, the actor apologised for attending the event in trainers, explaining that he didn't expect to win at all. He said his leather shoes had been flown ahead of him.
He apologised for his appearance, saying the prize was "totally unexpected". That job is left to the main-selection jury, which this year included five directors - two of them women - and was headed by Pedro Almodóvar.
But he appeared emotional when discussing how much he had loved Grand Prix victor BPM, which tells the story of activist group Act Up and the lack of government support for Aids sufferers in the 1990s.
At the closing press conference of the festival, Jessica candidly admitted that she wasn't impressed with how women had been portrayed in the films she saw and how the industry needs more female storytellers to create more authentic female characters.