The obvious inspiration for Sophie Barthes’ freshman feature is Charlie Kaufman, and “Cold Souls” will inevitably be seen as a sort of combination of “Being John Malkovich” and “Eternal Sunshine of the Spotless Mind.” But in fact the mood is different; the approach is more sedate and contemplative, and Barthes opts less for the flamboyantly bizarre than Kaufman does, preferring a ruminative matter-of-factness instead. And while the result has a certain quirky charm—mostly due to its star—the overall effect is rather pallid.

The star is Paul Giamatti, who plays a version of himself, an actor of his name rehearsing a production of “Uncle Vanya” in New York and feeling stressed and unsatisfied in his work. Hearing about a service that extracts one’s soul and puts it in storage to free you from the emotional baggage it carries, he goes in for a consultation with the firm’s head honcho, Dr. Flintstein (David Strathairn), who persuades the desperate fellow to give the procedure a try. Soon Giamatti is soulless and less antsy, but also hapless in his craft.

So he returns to the good doctor and is offered the chance to have another soul—chosen from a catalogue the firm obligingly provides—inserted into him. He selects that of a Russian poet, which seems exactly the thing for him, but before long his performance has taken on extravagant dimensions, he begins having weird dreams, and when his wife (Emily Watson) finds out what he’s done, she’s understandably peeved.

The actor’s difficulties link his story up with the second thread of the story, involving Nina (Dina Korzun), a Russian “mule” who brings black-market Russian souls to America, literally inside her. When her thuggish boss’s actress-girlfriend demands the soul of an American star to bolster her career, he has her steal Paul’s and bring it to Russia, where it does in fact improve her soap-opera turn (probably because she’s told it’s Al Pacino’s). But Giamatti, wanting his soul back, is eventually forced to link up with Nina for a dangerous mission to Russia to retrieve it. Things do not go smoothly there, and though the picture maintains a wry sense of humor in these latter stages (as when the duo kidnap the girl and exchange souls using an instruction manual), the tone grows increasingly somber and sad, especially in spinning the tale of the Russian soul’s original donor, a pathetic woman who worked in what amounts to a sweat-shop.

It’s that mixture of the quirkily funny and the poignant that makes “Cold Souls” distinctive, but also diminishes its overall effectiveness. Some scenes, like the extended conversations between Paul and Strathairn, have a dry, understated wit that’s very winning. (A good deal is made of the peculiar shape and size of Giamatti’s soul, which comes out looking like a deformed bean or chickpea, and a scene in which it’s dropped on the floor and has to be carefully searched for is good lowbrow slapstick.) But others, like the rehearsal sequences (with Michael Tucker as the harried director), are overdone and don’t quite work. And still others—those involving the Russian soul-trafficking, especially—have no particular quality at all, serving only to push the plot mechanically forward.

Then there are the darker, brooding moments, mostly in the Russian material but occasionally in the earlier stages too, that seem at odds with the humorous tone elsewhere. The picture’s all about the jostling and mixture of these disparate tones, of course, but the combination never settles, partially because the construction of the script doesn’t achieve the sort of zany logic a piece like this demands (what amounts to the epilogue, in which Homeland Security soldiers and a hedge fund officer are suddenly brought in, seems no more than a desperate device to tie up the narrative). The movie moves in fits and starts, and while there are incidental pleasures along the way, it never fully gels or cuts very deep.

One aspect of it, though, is an unalloyed joy—Giamatti. He, unlike the film, juggles the goofiness and poignancy gracefully in what’s easily his best performance since “Sideways,” and his willingness to allow much of the jokes at his own expense is charming. Apart from Strathairn, who’s perfect as the owlish, unflappable executive, the others don’t add much, with Korzun’s impassivity in particular failing to register. Technically matters are pretty ordinary, too—the production design lacks imagination (the whole extraction and re-insertion process is blandly familiar MRI stuff), and while Andrij Parekh’s cinematography captures the bleak, wintry outdoor images (especially in the Russian scenes), it’s never imaginative in any truly striking fashion. Nor does Dickon Hinchliffe’s score come across as particularly engaging.

And their work is characteristic of what “Cold Souls” has to offer. The premise is very promising, but Barthes doesn’t milk its potential, and even Giamatti’s elfin persona isn’t enough to make up for that.