The Palme d’Or at the Cannes Film Festival was awarded on Saturday to “Anora,” a giddily ribald picaresque from the American director Sean Baker about a sex worker who marries the son of a Russian oligarch — and things get very messy.

A critical favorite, “Anora” takes a nonjudgmental attitude toward its protagonist, played by Mikey Madison in a go-for-broke breakthrough performance that critics have praised. George Lucas, who received an honorary award at the ceremony, presented the Palme d’Or. Baker hugged Lucas and thanked the jury before blurting out, “I really don’t know what’s happening now.” He dedicated his award to “sex workers past, present and future — this is for you.”

The ceremony, which took place in the Grand Lumière Theater in the festival’s headquarters, opened with a spoof of the opening crawl of the original “Star Wars.” When Lucas eventually took the stage, he received a thunderous standing ovation. The applause grew even louder when Lucas’s longtime close friend Francis Ford Coppola appeared to present Lucas with an honorary Palme d’Or. Coppola, who referred to Lucas as his “kid brother,” was at the festival with his epic “Megalopolis,” which screened in the main competition and did not win anything.

The competition jury, led by Greta Gerwig, gave a special award to the gripping Iranian tragedy “The Seed of the Sacred Fig,” about a small family that comes violently undone just as the Women, Life, Freedom protest movement in Iran is igniting. The director, Mohammad Rasoulof, who fled the country right before the festival opened, accepted the award in person. On May 13, he announced on Instagram that he had left Iran after being sentenced to eight years in prison for his movies; he was also to be fined and whipped, and have property confiscated.

The Grand Prix, the festival’s second-highest honor, was given to “All We Imagine as Light,” from the Indian director Payal Kapadia. A gentle drama about three women coming to terms with one another and their own desires in contemporary Mumbai, “All We Imagine as Light” was another critical favorite. In Kapadia’s acceptance speech, she thanked the three leading actresses, whom she brought onstage with her, as well as all of the workers who make the festival run.