Diane Kruger won best actress for her first German-speaking part in "In the Fade", as a woman trying to put her life back together and get justice after her husband and young son are killed in a bomb attack. Having witnessed the integrity and dedication that you bring to every job, I'm over the moon to see you getting the recognition you deserve.
Kruger and Jackson ended their decade-long relationship in July 2016, saying in a statement at the time that they "decided to separate and remain friends".
"I can not accept this award without thinking about anyone who has ever been affected by an act of terrorism and who is trying to pick up the pieces and go on living after having lost everything", the actress said.
The film, a savagely amusing takedown of political correctness and the things we choose to hang in art galleries, had premiered to strong reviews - but even director Ruben Ostlund was shocked as he picked up the award, shouting, "Oh my God, oh my God!"
Iran participated with five films at this year's Cannes Festival (May 17-28) which marked the 70th anniversary of the event, and won three awards.
Triple Oscar nominee Joaquin Phoenix won best actor for playing a traumatised hitman in Lynne Ramsay's ultra-violent "You Were Never Really Here".
The actor wore sneakers on stage as he collected the prize. He apologized for his appearance, saying the prize was "totally unexpected".
"BPM (Beats Per Minute)', which was widely tipped for the Palme, was awarded the Grand Prix while Russian director Andrey Zvyagintsev had to be content with a jury prize for 'Loveless".
This year's feature films jury was headed by writer/director Pedro Almodóvar and included writer/director Maren Ade, actress Jessica Chastain, actress Fan Bingbing, actress/writer/director/singer Agnès Jaoui, writer/director Park Chan-Wook, actor/singer Will Smith, writer/director Paolo Sorrentino, and composer Gabriel Yared. The award recognizes a strong film that missed out on the Palme d'Or.
The jury also presented a special prize to celebrate the festival's 70th anniversary, to actress Nicole Kidman.
Almodovar said: "I loved the movie".
Kidman wasn't at the French Riviera ceremony on Sunday night but sent a video message from her home in Nashville, Tennessee.
Palme d'Or victor Ostlund exclaimed "Oh my god!"
He fake-cried and said in halting French, "merci beaucoup madames et monsieurs".