In one of A Complete Unknown’s wonderful musical scenes, Bob Dylan (Timothée Chalamet) and Joan Baez (Monica Barbaro) perform together at the Newport Folk Festival in 1964. They have had a tumultuous relationship and now Joan barely tolerates Bob, snarling at him when they have to speak.

They sing Dylan’s ‘It Ain’t Me Babe', their voices flowing together so beautifully that you could miss the potential chill of the lyrics, the emotionally avoidant goodbye from a person not willing to commit. “You say you're lookin' for someone/ Who'll promise never to part/ Someone to close his eyes for you/ Someone to close his heart/ Someone to die for you and more/ But it ain't me, babe/ No, no, no, it ain't me, babe/ It ain't me you're lookin' for.”

In the film, we know that Baez, having recently accused Dylan of being an “asshole”, has understood the lyrics for a while. But we see that offstage, Dylan’s on-again off-again girlfriend Sylvie (Elle Fanning playing a version of Suze Rotolo) only fully understands them for the first time. Part of her is jealous of his musical connection and previous entanglement with Baez, but that’s just a distraction. She knows she can’t ever have Dylan. She’s been trying, for years, but listening to ‘It Ain’t Me Babe’ makes her realise that she can’t keep loving someone who does not want to be known.

It's this struggle between Dylan’s fame and his resistance to being possessed that fuels James Mangold’s biopic. Set over four years, we meet the 19 year-old Dylan when he visits his icon Woody Guthrie (Scoot McNairy) in hospital, where Guthrie is receiving care for his Huntington’s disease. Longtime pal Pete Seeger (Edward Norton) is by Guthrie’s bedside, and when the young Minnesota blow-in plays a song he has written for Woody, the two men are struck down to the ground – as was I. Timothée Chalamet’s performance of Dylan’s songs sparks with authenticity, charisma and soul-changing creativity. You can feel the energy shift as he sings, his lyrics feeling prophetic, his cadence making you hang on every word. There’s an irresistible quality to Chalamet’s Dylan – and Mangold’s film becomes about how Dylan comes, at once, to understand this power and to resent how it makes everyone want something from him.

Initially, unknown Dylan has to struggle for ownership over his songs, which are covered by more famous artists such as Baez. But when Dylan starts achieving fame and success, everyone wants something from him. Baez wants to sing his songs, and wants more affection that he can give. Seeger, though sweet and supportive (played to perfection by Edward Norton), recognises Dylan’s talent and needs him to become and then remain the tentpole act for his beloved Newport Folk Festival.

Fans have a vampiric need for him, trying to absorb his genius as if it were contagious. And while Sylvie simply wants to love him, she wants to know more about him than Dylan’s deliberately cultivated mystique allows. At one point, Sylvia and Dylan are living together, but she reveals she knows nothing about his family, his childhood, his past. Dylan came to New York like a mysterious troubadour, wanting to impart his wisdom and philosophy through his songs without further explanation that might dilute their power.

Dylan’s resistance to definition, and to relationships he views as transactional, creates an interesting dilemma for Mangold, who has to make audiences care about a man who is prickly, reticent, deliberately unknowable and often consciously unlikeable. Mangold gives us glimpses of who Dylan is: his letters to Johnny Cash (based on the men’s real-life correspondence) show us how he relaxes and opens up around someone he admires. And his songs, of course, act as a truly magical insight into his soul, displaying a cultural awareness, emotional intelligence and philosophical mindset that his sullen, reticent demeanour often belies.

He wants his music to speak for itself, and it does – Dylan’s performance of ‘The Times They Are A-Changing’ at Newport is remarkable and emotive. It’s clear from the faces in the crowd – and thr immediate, innate understanding of the song they show – that he has captured a feeling they couldn’t articulate. Mangold’s subtle references to the cultural and political context sets the scene up beautifully – news clips of the Cuban Missile Crisis play in the background of early scenes, the streets of New York become unnervingly empty as people fear the end of the world is at hand.

Dylan’s fans’ sense of awe around his talent, his mystique and his ability to summarise the feelings of a generation in turmoil inspired at times fierce loyalty – but while they were open to hearing that the times were a-changing, they were less willing to embrace those changes. A Complete Unknown shows how a generation of folk fans (Seeger and his peers included) demanded genre purity – and this was yet another form of control and ownership that Dylan resisted. When Dylan “turned electric”, the reaction was loud and enraged (Mangold take some liberties here, transplanting the infamous ‘Judas’ incident from Manchester 1966 to Newport in 1965 to illustrate the ire of the folk festival attendees.)

Chalamet is remarkable while singing, but elsewhere his Dylan remains a shadowy presence. Monica Barbaro is wonderful as Baez, and Fanning does well with an underwritten character who shrinks under Dylan’s inconsistency.

The film is very good on both Dylan’s experience of fame and the puritanical struggle within the folk scene of the time. But Mangold allows him to remain enigmatic – not only to his lovers and fans but to the audience. With a series of stunning musical performances at the heart of A Complete Unknown, it is only this characteristic emotional detachment which will prevent the film from becoming a cinematic classic.

• In cinemas now. Watch the trailer below.