Slowly but surely, the gentleness of Jim Jarmusch’s lovely new film steals up on you. It has an almost miraculous innocence. I can’t remember when I last saw a movie whose adult characters had so much simple, unassuming goodness, goodness that breaks everything in the modern culture rulebook by going unironised and unpunished. And Adam Driver’s face is something to fall in love with. An Easter Island statue reborn as a sensitive, delicate boy.

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It is about a man called Paterson, played by Driver, who works in Paterson, New Jersey; the coincidence underscores his matter-of-fact hometown loyalty without any great emphasis, though it echoes a similar alignment in the epic poem of that name, and about that place, by William Carlos Williams. Paterson has evidently served in the US military and is now a bus driver. He is also a poet on his own time (an admirer of Williams, in fact), thoughtfully writing in a notebook during breaks. His simple, accessible verses appear on screen in squiggly handwriting as he works. He is not supposed to be a genius, but neither is his work hilariously awful or inadvertently revealing, as it might be in another type of film.

Paterson is very happily married to the beautiful Laura (Golshifteh Farahani) who stays at home, pursuing her talents: painting, decor, cooking. She begs Paterson for money so she can buy a guitar and pursue her dream of being a country singer. But again: this guitar does not bring the financial ruin or mortification that you might expect. The point is that Laura is rather good and her plans are not that implausible. At all times, we laugh the way Paterson laughs – with Laura, not at her.

In the evenings, Paterson walks their English bulldog Marvin and has a quiet beer where he chats with barkeep Doc (Barry Shabaka Henley) and helps sort out the unhappiness of some other bar regulars: young former lovers Marie (Chasten Harmon) and Everett (William Jackson Harper). And his life continues in its utterly happy, non-careerist way until he is confronted with a terrible loss, which appears at first comically absurd but is very serious.

Facebook Twitter Pinterest Happy home … Adam Driver and Golshifteh Farahani. Photograph: Mary Cybulsky/Window Frame Films

This is a real place with real landmarks, yet Jarmusch can’t help reconfiguring it into one of the unreal, ghost-town sites of his imagination. Paterson will walk streets that are weirdly uninhabited, except for sudden, startling cameo-apparitions. It is not that far from the ruined Detroit of his vampire fantasy Only Lovers Left Alive (2013) and Paterson’s easy self-reliance is like Forest Whitaker’s in Ghost Dog: The Way of the Samurai (1999).

There is a very real, nuanced moment when, listening in to his passengers’ conversation, Paterson starts smiling at the machismo of a couple of bragging, sexist guys – but a female passenger frowns at them while getting off: Paterson sees that and thoughtfully corrects his own smirk.

Adam Driver’s Paterson is robust, candid, ingenuous – 'without side', as the English say

Yet so much of the rest of the movie is not quite real, or perhaps it is rather that Jarmusch does not replicate reality in the way other film-makers do. Paterson is walking the dog when a crew of gangbangers surreally roll up, yet there is no tension or confrontation: they just ask (admiring) questions about his pet.

The unreality extends to Laura’s persistent, fateful questions about making sure Paterson’s poetry gets out to the public, and worrying that he has made no copies. Both have evidently never considered or even heard of public performance or poetry slams, or sending his work to magazines, or self-publishing digitally. No, all Laura means is Paterson going to a store and getting his poems photocopied – though, unlike her technosceptic husband, she has a smartphone and could presumably photograph them all herself in five minutes. Yet you accept all this as part of the tender protective unworldliness that Jarmusch creates for his characters like an almost magic canopy: Paterson’s work exists in a pre-Gutenberg state and this meshes with Jarmusch’s film-making vernacular.

Adam Driver’s Paterson is robust, candid, ingenuous – “without side”, as the English say. Or, as American soldiers say: he is squared away. That equine, distinguished face is far from the villainy of the new Star Wars movies. He sometimes looks as if he could be any age from 27 down to 17; it is an open and generous face, clouding heartbreakingly at the moment of loss, clearing wonderfully at a final, mysterious, serendipitous encounter. He has never been more beguiling as an actor.