Triet called being only the third woman to win "surprising" and said the decision was encouraging for the future.
"We're at the dawn of deep-seated changes in this respect," she said after winning.
Triet used her award speech to criticize how the protest against pension reforms in France "has been denied and repressed in a shocking way" and said more space needed to be made for young filmmakers to be able to make mistakes and start over.
Triet, who had previously been nominated for Sibyl in 2019, won the prize over veteran directors like Hirokazu Kore-eda, Ken Loach and Wim Wenders, all of whom have at least one Palme d'Or under their belts.
Jane Fonda, who introduced the award, said that one day it would be normal for women to win, not historic.
"We have a long way to go. But still, we have to celebrate change when it happens," said the film icon and activist.
The Grand Prix, the second-highest prize after the Palme d'Or, went to British director Jonathan Glazer's The Zone of Interest, about a family living next to Auschwitz.
"It's so important that the film goes out into the world and hopefully has an effect and gets people talking about the themes that are in the film," Glazer said after winning.
However, the award for best female actor went to Merve Dizdar, who plays a teacher in an isolated village in Turkey in Turkish director Nuri Bilge Ceylan's About Dry Grasses.
Best actor went to Japan's renowned Koji Yakusho, who plays a toilet cleaner in Tokyo who is content to just read books and listen to music in German director Wim Wenders' Perfect Days.
Fallen Leaves by Finland's Aki Kaurismaki, who was back in the competition after more than a decade, took the jury prize.
The award was accepted on his behalf by the two main stars of the tragicomedy that follows a budding romance between a quiet young woman and a heavy-drinking sandblaster.
While introducing best screenplay, John C Reilly showed his support for striking Hollywood writers with roughly a minute of wordless mimicry before saying: "What we just experienced is what a movie would be like without screenwriters."
That prize went to Yuji Sakamoto for the Japanese entry Monster, directed by Hirokazu Kore-eda, which follows a series of misunderstandings surrounding two schoolboys' friendship.
On Friday, Anatomy of a Fall also won the top prize at the Palm Dog awards for border collie Messi's performance as Snoop in what organizers said was the toughest competition yet.
This year's closing movie was Pixar's Elemental, an animated feature about a city where the four elements live together, featuring the voices of Leah Lewis and Mamoudou Athie.
