Fyodor Dostoyevsky’s “White Nights” has been adapted to film by Luchino Visconti (with the same title), Robert Bresson (as “Four Nights of a Dreamer”), and now, the Indian director Sanjay Leela Bhansali. The novella’s mood-swinging tale is an ambitious choice of material, but “Saawariya,” Mr. Bhansali’s follow-up to his 2005 success, “Black,” falters at making the romantic tragedy sing through its pangs.

“Saawariya” is about the particular pleasure and pain of partly requited love. A slightly goofy musician named Raj (Ranbir Kapoor) arrives penniless in a storybook town that resembles Venice, by way of old New Orleans. The bowler-clad songster spots a distressed woman during a nocturnal jaunt, and he’s smitten. He learns her name only after their pas de deux of apprehension and flirtation, but the delicately beautiful Sakina (Sonam Kapoor) turns out to be hooked on her own obsession, a lodger (Salman Khan) who left her grandmother’s house but promised to return.

As in Visconti’s stylized black-and-white version, the hushed alleys and bridges are as much characters in the film as the almost-lovers, and they provide the perfect setting for the pair’s missed connection. But, with characteristically elaborate set design, Mr. Bhansali also opens up the show with some grander, emerald-hued sets. Notable are the (genteel-looking) red-light district that’s home to the buxom prostitute Gulab (Rani Mukherjee) who’s tracking Raj’s story, and the surreally light-flooded house where Raj boards with a tough old broad (Zohra Sehgal).

In flashback we learn how Sakina fell for the lodger right under her blind grandmother’s nose. He’s a smolderer, all right, and the callow Raj does his best to stake his own spot in Sakina’s heart. His puppy-dog pursuit takes the familiar cinematic form: He comes up with clever riddles, takes impulsive trips to shadow-dappled roosts with town panoramas, and, of course, leaps onto the piano at a bar to rally the crowd with his aw-shucks big love.

There’s probably a reason it’s taken until now to mention the music in this Bollywood film. Raj has a couple of adequate, yearning solos, and there are two good head-bobbing extravaganzas of synchronicity (one with Gulab and colleagues, one with men interrupted at prayer). But for a movie that’s touted as the first in a forthcoming wave of Hollywood-backed Indian films, “Saawariya” feels (comparatively) subdued, floating along rather than bursting forward.

That’s not a deal-breaker if you’re expecting the mood of disappointment inherent to the story, but the thwarted lovebirds at the center of the attempted magic are only intermittently compelling. Ms. Kapoor is sweet, and arresting in close-up, but tends to fade from memory. Mr. Kapoor throws his heart into playing the charming minstrel and good guy, and he braves ridicule in a scene featuring a peekaboo jig of joy in a towel (and, briefly, not even that), but he lacks spark, as well as any real chemistry with his costar.

The difference is obvious whenever Ms. Mukherjee and Mr. Khan, Bollywood veterans both, appear on-screen. Each Kapoor possesses the requisite Bollywood family pedigree, but only Mr. Khan and Ms. Mukherjee know how to switch on the star power, even in their sideline roles. The Kapoors’ “naïve young lover” routine looks bland alongside the sensual intensity packed by Ms. Mukherjee and Mr. Khan into a surging gaze. Even Ms. Kapoor seems more alive in her scenes with Mr. Khan.

“Saawariya” might simply be at odds with the inconsolable strains in the source material, and perhaps Mr. Bhansali should have felt freer in departing from its boundaries. (At a trim 147 minutes, he was obviously holding himself back a little, by Indian marathon-musical standards.) When the movie illustrates the way unattainable romance can fall short of one’s desires and expectations, it may not be in quite the way the filmmaker intended.