“The Monuments Men,” a film that George Clooney co-wrote, directed and stars in, continues his long-standing — even heroic — effort to preserve a certain kind of movie in the American filmmaking canon. From the films he’s directed (“Confessions of a Dangerous Mind,” “Good Night, and Good Luck,” “Leatherheads,” “The Ides of March”) to many he’s starred in, Clooney has evinced a fealty to the classical, even old-fashioned kind of film that, we’re so often depressingly reminded, Hollywood doesn’t make anymore.

With “The Monuments Men,” Clooney looks to the grammar of World War II thrillers, caper comedies and standard sentimental uplift to tell the story of the U.S. Army’s Monuments, Fine Arts, and Archives program, wherein a group of art historians, architects and artists sought to save and preserve artworks looted by the Nazis during the war. Rather than a ragtag team of misfits and rejects, these were gentlemen and scholars tasked with preventing Adolf Hitler from amassing the masterpieces of Western art for his planned Fuhrer Museum; as the war came to a close, their mission shifted to saving those works from destruction — or confiscation by the Soviet army, which intended to abscond with them as early reparations.

It’s a pip of a story, and Clooney cuts a dashing, Gable-esque figure as the group’s leader, Frank Stokes (based on real-life Monuments Man George Stout), who rounds up a group of bookish, out-of-shape academics and professionals, sends them to basic training and sets them loose amid the wreckage of Normandy, St. Lo and the Bulge. “The Monuments Men,” which Clooney wrote with producing partner Grant Heslov, starts out with funereal solemnity — gunshots accompanying close-ups of a fine 15th-century painting turn out to be nails being struck while the Ghent Altarpiece is dismantled and spirited away for safekeeping. But soon enough the mood turns jaunty, as Stokes’s men fan out across the charred countryside to save what Stokes calls, in one of several why-we-fight speeches, “our culture and way of life.”

These tonal shifts bedevil the rest of “The Monuments Men,” which despite its absorbing story never quite hits its stride either as a stylish wartime thriller (of which John Frankenheimer’s similarly themed “The Train” will forever be the epitome) or jocular lark (“Ocean’s Altarpiece,” anyone?). Ever the shrewd captain, Clooney has assembled his own cast of men who are monuments: John Goodman, Matt Damon, Bill Murray, Bob Balaban, Hugh Bonneville and “The Artist’s” Jean Dujardin play the team members, with an assist from Cate Blanchett as a woman working in Paris’s Jeu De Paume museum. The group’s most poignant figure, a Jewish soldier from New Jersey who harbors a special connection to a particular Rembrandt painting, is played by the least well-known cast member, Dimitri Leonidis. (His character is based on former infantryman Harry Ettlinger, who also appears in the book by Robert Edsel from which “The Monuments Men” was adapted.)

All too soon, this promising ensemble breaks into dyads that go their separate ways, resulting in a film that often feels like an anthology of small buddy comedies that never quite jell. (Murray and Balaban come closest to developing genuine chemistry, especially during an affecting moment set to the melancholy “Have Yourself a Merry Little Christmas.”) Just when one team begins to get a scheme off the ground, the film shifts gear and locale to check in with someone else, sometimes introducing a note of grim comedy. But lest the audience be tempted to think “The Monuments Men” is going the way of “The Dirty Dozen” and its rough-and-tumble peers, Clooney is always on hand to deliver yet another stirring sermon on art-with-a-capital-A and why it’s not just important, but worth risking life and limb for.

Sam Epstein, John Goodman, George Clooney, Matt Damon and Bob Balaban star in director/writer Clooney’s earnest “The Monuments Men.” (Claudette Barius)

That’s a lot of moving parts to keep in balance, and “The Monuments Men” often lets the schematic gears show, succumbing to threadbare formula and sentimental cliches rather than taut, sophisticated drama.

Clooney finally works up a convincing degree of tension once Stokes and his men face multiplying hurdles in their race against the clock, the Nazis and the Soviets. And he does a commendable job of ensuring that the context, meaning and all-too-real human stakes of the search are never far from mind: Among the most moving scenes in “The Monuments Men” is one in which Damon’s character — a wholesome art restorer named James Granger — hangs up a lone portrait that he’s managed to recover in the barren apartment of its Jewish owner, as if one painting can stem an incalculable tide of devastation and loss. Later, Clooney juxtaposes a shot of a burned Picasso with a barrelful of human gold-capped teeth.

Those moments lend heft to what is otherwise a stolid, modestly entertaining drama about an eminently deserving moment in history. “The Monuments Men” looks terrific, with cinematographer Phedon Papamichael shooting the mostly German locations with a lovely, desaturated patina. The film exists in a heightened netherworld between immersive realism and carefully set-dressed theatricality.

If Clooney and Heslov feel the need to underline to a fault their points about the sanctity of Western culture and society and way of life, and if “The Monuments Men” never overcomes its unwieldy structure and unevenness of tone, the film still manages to make a profound, even subtle point: that Hitler’s darkest impulses and annihilating reach extended from human beings to history itself. “The Monuments Men” drives that startling truth home, imperfectly but with chilling clarity.

★ ★ ½

PG-13. At area theaters. Contains images of smoking and wartime violence. 119 minutes.