A shaggy-dog romance that shouldn’t work but does, Jesse Peretz’s adaptation of Nick Hornby’s 2009 novel is one of the season’s more pleasant surprises. Like many of Hornby’s plots, that of “Juliet, Naked” has a rock connection, but it’s treated with a disarmingly flippant air.

Such an attitude is, however, one with which Duncan Thomson (Chris O’Dowd), a highly opinionated, incessantly caustic teacher of film and television studies in a lesser British college, would vehemently reject. He’s probably the world’s most devoted fan of Tucker Crowe, an obscure American singer-songwriter who made but one album, “Juliet,” before abruptly walking off stage in mid-gig a quarter century ago, never to reappear. Duncan is certain that Crowe was a genius for the ages, and broadcasts his view over a website filled with Crowe ephemera and rumors that has a paltry number of followers. He runs the site from a room in his house that’s a virtual shrine to Crowe, the walls decorated with posters, ticket stubs, magazine articles and album covers.

But it isn’t really Duncan’s house: it belongs to his long-time, and long-suffering girlfriend Annie Platt (Rose Byrne), who helps run the town of Sandcliff’s Seaside Museum. It’s a thankless job, thanks to a pushy boss who rejects any interesting suggestions, and she’s grown increasingly tired of Duncan’s idolization of Crowe, whose songs she does not find particularly remarkable.

A turn in the Duncan-Annie relationship begins when there arrives a parcel in the mail containing a CD of the original demo recording of the “Juliet” album—the titular “naked” version—from an anonymous source. Annie listens to it before Duncan gets home—which irritates him no end—and then, after he writes about it profusely and admiringly on his site, posts a comment saying how dreary it is. She gets an e-mail in reply agreeing with her assessment. The sender claims to be none other than Tucker Crowe, and it actually is—a fact she keeps to herself.

Thus begins their correspondence. Tucker (Ethan Hawke), it turns out, is a rumpled, shaggy-haired, big-bellied guy living in his last ex-wife’s garage, puttering in the garden but otherwise doing little but enjoying the company of Jackson (Azhy Robertson), his young son by her. Tucker has children by two earlier wives as well, but has minimal contact with them until a pregnant daughter studying at a college in the States (Nina Sosanya) visits him. The stay is awkward, but it makes him more interested in connecting with his rather extended family—which he why he and Jackson come to England when his daughter gives birth. He suggests that he and Annie meet, and they do. Meanwhile Duncan has taken up with a new faculty colleague and has understandably been thrown out by Annie.

Things go fairly predictably from there, but in an amiably unforced way. The cast proves charming across the board, with even O’Dowd’s arrogant Duncan mellowing as he tries desperately to connect with Crowe, who is utterly uninterested in being celebrated—indeed, in music at all. Hawke plays him with a delightfully laid-back attitude, and he’s complemented nicely by Robertson, who does a sterling job of being an adorable tyke. Despite the fact that one can see most of the script’s turns from a mile away, the movie repeatedly comes up with amusing surprises, like a scene in a hospital room that feels like a nod to the famous stateroom episode from “A Night at the Opera.”

“Juliet, Naked” isn’t the slickest movie from a technical standpoint: though the locations are all nice (with Ramsgate standing in for Sandcliff) and cinematographer Remi Adefarasin employs them to advantage, it mirrors Hawke’s Crowe in being more than a mite ragged-looking, and the editing (by Sabine Hoffman and Robert Nassau) is a bit choppy too. And while Nathan Larson’s music is fine, the shards we hear of the early Crowe songs are nondescript—though that might well be the point.

Overall, though, in an era when most romantic comedies try too hard, it’s a pleasure to encounter one that’s content to coast along so agreeably as “Juliet, Naked,” the rare movie from producer Judd Apatow that’s worth watching.