Maybe it's an illusion, but Cannes always seems to end in a mad rush, as the festival's theaters squeeze in the last contenders for awards. (Two fresh competition films premiered on Friday, one day before the Palme d'Or will be handed out. Giving the jury time to think about its decisions is not a Cannes requirement.) Let's take the final four in turn.

Catherine Breillat's "Last Summer," her first feature since the more-or-less-autobiographical "Abuse of Weakness" 10 years ago, finds her returning to trademark mode of sexual provocation ("Fat Girl," "Anatomy of Hell"). Technically, it's a remake of the Scandinavian film "Queen of Hearts" (2019), although if my memory of that movie serves, this is a much more considered and cutting treatment, especially with regard to its ending.

Anne (Léa Drucker) is a lawyer who frequently defends rape victims and therefore knows a few things about power dynamics and how witnesses can be framed as liars—a skill that will prove useful in her personal life. Despite the obvious danger, she finds herself drawn into and perpetuating a sexual relationship with her 17-year-old stepson, Théo (Samuel Kircher), under the nose of her husband and his father, Pierre (Olivier Rabourdin).

Breillat is interested in a number of things here: testing viewers' discomfort, forthrightly depicting female desire (one of the sex scenes keeps the camera in tight closeup on Anne's face), defending the right to sexual hypocrisy. Still, "Last Summer" is pretty tame by Breillat standards, and I didn't for one second believe that these characters would ever get involved with each other. But perhaps the film deserves a bit of license on that point.

"Perfect Days" is Wim Wenders's second movie at Cannes this year, after the 3-D documentary "Anselm," an immersion in the work of the artist Anselm Kiefer. This fiction feature was shot in Tokyo (which looks sensational in the cinematographer Franz Lustig's electric palette) and is almost entirely in Japanese. Koji Yakusho plays Hirayama, a bathroom janitor who is not mute but for the most part doesn't speak. It wouldn't be at all surprising if Yakusho's understatedly physical performance wins an award on Saturday.

Much of the movie consists of simply watching Hirayama drive around Tokyo, clean bathrooms, play an ongoing game of tic-tac-toe with a mystery patron who leaves a sheet of paper in one of the bathrooms for him, and/or listening to the Animals, Nina Simone, or whomever else Wenders cares to drop on the soundtrack. (Lou Reed, naturally, provides the title.) Eventually Hirayama's niece (Arisa Nakano) shows up at his doorstep, and for a short stretch "Perfect Days" almost has a plot. The movie feels much more like a mood piece by the Wenders who made "Kings of the Road" and "Paris, Texas" than the Wenders who made "Palermo Shooting" (2008), the director's disastrous last foray into Cannes competition. But while black-and-white dream sequences add an element of mystery, "Perfect Days" finally feels a little slight.

Alice Rohrwacher's "La Chimera" is a late contender for the strangest and least classifiable film in competition. It stars Josh O'Connor as Arthur, an Englishman in Italy who becomes part of a group that makes money locating, digging up, and plundering Etruscan tombs, selling the antiquities to a mysterious figure called Spartaco (presumably as in the "I'm Spartacus" scene of "Spartacus"—it could be anyone, but isn't).

Rohrwacher ("The Wonders," "Happy as Lazzaro") has always had an oblique approach to narrative, and it takes a while watching "La Chimera" just to get a full sense of the scheme's implications. It takes no time at all, though, to see that this is a restlessly inventive film, mixing film stocks (Hélène Louvart did the cinematography) and aspect ratios and moving fluidly between dream logic and reality. The humor is offbeat (in the opening minutes, Arthur socks a sock salesman on a train, and there's a late set piece involving an art sale at sea that might well have wandered in from an "Austin Powers" sequel). I found "La Chimera" completely fascinating and utterly unstable. "Happy as Lazzaro" took me two viewings to appreciate, and I suspect that will be the case here too.

The title of Ken Loach's new drama, "The Old Oak," refers to the name of a pub that becomes contested territory in a town in the north of England in 2016. Longtime locals resent the decline of their former mining community and see a scapegoat in the recent influx of refugees from Syria. TJ Ballantyne (Dave Turner), the bar's owner, hesitates to provide assistance to the newcomers, wagering that the xenophobic locals pay his bills. But he warms to Yara (Ebla Mari), a photographer, who helps him see that an old value during the miners' union days—the idea that if people eat together, they'll stick together—could be the solution to closing a senseless rift.

Loach can be self-righteously didactic ("I, Daniel Blake," which won him his second Palme d'Or in 2016, disguised a nuance-free policy position as an existential statement), but "The Old Oak" is one of the stronger films of his long run with the screenwriter Paul Laverty, with whom he's worked since the late 1990s. That's party because it puts character first. TJ and Yara aren't simply pawns in society, but have genuinely complex motives influenced by their lives and by history. Regrettably, Laverty's penchant for turning what should be subtext into lengthy speeches hasn't totally gone away, and the cruelty visited on a dog feels like something he and Loach added just to up the misery factor (there are shades of the end of "Kes"). But this is still pretty powerful stuff.