First Night: The Exchange, Cannes Film Festival

In the twilight of his directorial career, Clint Eastwood continues to make some of his finest films. The Exchange (which mysteriously changed its title from The Changeling only days before its premiere in Cannes) is a magisterial piece of work.

Set in the late 1920s and early 1930s, it features a performance from Angelina Jolie which will almost certainly win her award nominations. She plays Christine Collins, a single mother with a nine-year-old son, Walter. One day, when she is asked to work overtime at a telephone company, she comes home to find Walter missing. Jolie conveys brilliantly the mix of anger, desperation and grief the mother feels as she tries to track down her son.

What starts as a missing-child melodrama turns into a riveting James Ellroy-style exposé of corruption in the LAPD. The mother is helped by Rev Gustav Briegleb, a crusading Presbyterian preacher (John Malkovich), as she tries to fight back against the authorities, who will go to extreme lengths to stop her besmirching their reputation.

Eastwood has never been known as a liberal, but it is hard not to see the film as an allegory about the present US administration. The politicians and cops in his 1920s LA are ready to imprison and torture their opponents. They are masters of media manipulation.

Jolie's Christine is the female equivalent to those upstanding heroes fighting against corruption that you find in old Frank Capra movies. "Never start a fight, but if you're in one, make sure you finish it," is her mantra. She represents an old-fashioned idea of American decency.

At times, this feels like film-making from another era. The pacing is leisurely. Eastwood doesn't use flashy effects or handheld cameras but his recreation of pre-war Los Angeles is spot on. Production and costume design are meticulous without drawing attention to themselves.

Occasionally, the narrative is a little contrived, but this is storytelling on an epic style. On one level, it is a thriller about mistaken identity.

There are hardboiled sequences echoing old Warner Bros crime dramas, some riveting courtroom scenes, and a horrific interlude in a mental institution.

The character turns are perfectly judged. Eastwood never loses sight of the emotions that are driving the story. At its core, this remains a drama about a desperate mother's quest for her missing son.

Thanks to her media profile, Jolie cuts such an absurd figure it is easy to forget how accomplished she can be. This is a performance of subtlety and power.

The Exchange won't be Eastwood's most successful movie. Its themes are far too dark. But, in its unfussy craftsmanship and emotional punch, it shows him still at the peak of his powers.