Cannes audiences just heard a clean, hard crack: the sound of the Coen brothers hitting one out of the park. Their new film is brilliantly written, terrifically acted, superbly designed and shot; it's a sweet, sad, funny picture about the lost world of folk music which effortlessly immerses us in the period.

The musical interludes are stunningly achieved: a pastiche chart single about President Kennedy and the moon mission brought the crowd I was among close to bopping in the aisles. This has something of Woody Allen movies like Sweet and Lowdown and Broadway Danny Rose; there's a playful allusion to Breakfast at Tiffany's and even a weird casting echo of Walter Salles's On the Road — and this movie is incidentally everything that dull film wasn't. But it is through-and-through a Coen brothers film, as pungent as hot black coffee.

Inside Llewyn Davis recounts a desolate week in the life of a fictional singer-songwriter of pre-Judas folk music in early-1960s New York: Llewyn Davis — a quietly angry, depressed and penniless young man, dragging his guitar from apartment to apartment, sleeping on couches, annoying everyone, unsure whether to continue in a world that does not understand him, and preparing to abandon his dream and returning to work in the merchant marine. There comes a time with any artist, when failure has become too painful and losses have to be cut. Has that time come for Llewyn Davis? He is played with cool, shrewd, watchful restraint by Oscar Isaac, with longish black hair and an unkempt beard, looking for all the world like a young Martin Scorsese. The name "Llewyn" with its Welsh associations, of course deftly brings the word "Dylan" into our minds, although the question whether Llewyn is supposed to be a specific fictional variant of the great troubadour is resolved in the final moments. It could also, at a second subconscious remove, suggest the doomed figure of Dylan Thomas, who succumbed to celebrity and hard liquor in the United States. Llewyn has been attempting a solo career, having just split from his performing partner, with whom he produced a poignantly unsuccessful and heartrendingly entitled LP, If I Had Wings, and the well-observed cover design is a joy, although the Coens are not looking for big laughs, like Spinal Tap or the folk spoof A Mighty Wind, but elegantly asserting design mastery, allowing us to savour how their exterior shots of New York do look exactly like these LP covers. Now he has a record of his own, Inside Llewyn Davis, unsold copies of which take up a big heavy cardboard box in his agent's office, a box he is brusquely invited to take away with him. Again the title is ironic: these moody opaque songs don't get us anywhere close to being "inside" the singer's mind.

Inside Llewyn Davis: 'This is real genius' - video review Remote Master

He has a tense relationship with a successful folk duo, played by Justin Timberlake and Carey Mulligan, and strikes up a quick friendship with another would-be folk star, Al Cody, gloriously played by Adam Driver, whose booming single notes during the "Hey Mr President" recording session make that scene such comedy gold. Llewyn figures he might be able to make an audition in Chicago, and to that end shares a car with a smoulderingly Kerouac-y poet, played by Garrett Hedlund and a pompous jazz musician played by John Goodman with a habit that keeps him detained a long time in the men's room.

The film has some classic Coen tropes: wide establishing shots of eerily empty spaces and interiors with receding perspective lines, deadpan faces, querulously bespectacled old ladies and the mandatory old guy in a semi-darkened office. But the authorial signature is not quite so emphatic as of old, and the Coens treat themselves to a lot of straightforwardly funny lines. Ultimately, the heartrending thing about Inside Llewyn Davis is its meditation on career success and career failure, and the unknowable moment when the one turns into the other. The Coens allow us to be unsure about the point of Llewyn's music: is it obviously brilliant and destined for success? Or is the point rather that he is talented, but not in a way that guarantees triumph? Llewyn is at least partly depressed about the way mediocrities do well in this world: silly singing acts in cable-knit sweaters. He could just be ahead of his time, but will the imminent arrival of Bob Dylan mean that his kind of difficult music will finally get what it deserves? Or just consign him even more brutally to an honourable second place? The intense sadness that permeates every chord and every note of his music, could be a desperate requiem for his own dreams, his own musical career. What an intense pleasure this film is, one of the Coens' best, and the best so far at Cannes.