Every Wes Anderson film is filled with musical delights, from offbeat songs to unexpected score cues, and “The French Dispatch” is no exception.

Composer Alexandre Desplat and music supervisor Randall Poster are among the first to read any new Anderson script. “He and I have been corresponding with music since the day we met,” says Poster, “and over the course of 25 years there’s a lot of musical history that we draw upon for different projects.”

“The French Dispatch,” an homage to the New Yorker magazine’s traditions and writers, was special for the Paris-based Desplat because the film is based in “a fantasized France,” as he puts it, a not-quite-real France as seen through Anderson’s unique prism.

Desplat scored the opening sequence (with Bill Murray as the editor) and two of the three episodes in the film, about an imprisoned artist (Benicio del Toro) and a police commissioner (Mathieu Amalric) whose son is kidnapped. He drew inspiration from late 19th- and early 20th-century French pianist-composer Erik Satie, “the French surrealist rebel character” whose early minimalist pieces are strangely haunting.

“It’s a handful of people at a newspaper in the past, a little place, like a postcard from the ’60s, so there was no reason for the score to be lush or huge,” Desplat explains. “We needed something sparse and clear, and solo piano seemed to be the best option.”

He asked his friend, the Grammy-nominated pianist Jean-Yves Thibaudet, to record the piano parts. They had earlier collaborated on the 9/11 movie “Extremely Loud & Incredibly Close.”

It was mid-pandemic, however, so Thibaudet recorded his parts in the U.S. and the other musicians were recorded at London’s Abbey Road. The more lighthearted moments, especially in the opening and the bizarre, chase-filled finale, feature an offbeat collection of instruments from harpsichord to banjo and tuba.

Three of Desplat’s 11 Oscar nominations are for Anderson films (including “Fantastic Mr. Fox” and “Isle of Dogs”) and he won for one, 2014’s “The Grand Budapest Hotel.”

As for the many songs in “French Dispatch,” Poster notes that “we were focused on using French music,” including a Charles Aznavour ballad (“J”en déduis que je t’aime”) and a remake of the 1965 French hit “Aline” by English musician Jarvis Cocker. The latter anchors the middle episode, with Timothée Chalamet as a student revolutionary and Frances McDormand as the writer who profiles, and sleeps with, him.

“It’s a song that Wes and I have really admired over the years,” Poster says, and they cast Cocker as the singer Tip-Top (a thinly disguised version of Christophe, who wrote and sang “Aline”). “We had so much fun recording ‘Aline’ we thought we’d make a Tip-Top record, and we did,” Poster says.

So in addition to the “French Dispatch” soundtrack, a companion album has been released of classic French songs (originally performed by everyone from Serge Gainsbourg to Brigitte Bardot) performed by Cocker in character as Tip-Top.

Film music buffs will also recognize excerpts from scores by French composer Georges Delerue and Italian composers Ennio Morricone and Mario Nascimbene threaded throughout the narrative.