Winston Churchill famously said that meeting Franklin Roosevelt was like opening your first bottle of champagne and knowing him was like drinking it. But there’s nary a hint of sparkle or fizz in “Hyde Park on Hudson,” a strangely dour period piece that paints FDR as an inveterate womanizer and his pre-war introduction to the king and queen of England as a sour comedy of manners.

Perhaps that’s because the story is told from the perspective of Daisy Suckley (Laura Linney), a dowdy, spinsterish cousin of the president who’s invited to Hyde Park, the tiny New York town where FDR (Bill Murray) spent time away from Washington at the ramshackle house of his mother Sara Ann (Elizabeth Wilson), to lift his spirits. Documents discovered after Daisy’s death disclose that during her increasingly frequent visits, Roosevelt in effect made her his mistress, even though his wife Eleanor (Olivia Williams) was in residence too. And Daisy was distressed to learn that she wasn’t the only one—she shared the president’s off-time with his efficient secretary Missy (Elizabeth Marvel) as well. But she (and Missy) apparently came to terms with that.

One expects that a portrait of President Roosevelt as a ladies’ man could be the stuff of high comedy, particularly as the role of FDR has fallen to Murray, whose skill in garnering laughs is well known. But as directed without much flair by Roger Michell, the script by Richard Nelson downplays the potential farce in favor of weak-tea humor, centered on the visit of young King George VI (Samuel West) and his wife Elizabeth (Olivia Colman), who have come to America to curry favor with the president and the people in expectation that their country will need assistance when war against Germany inevitably comes. (The year is 1939.) Much is made of the royals’ discomfort at being housed in a cramped upstairs bedroom with unflattering prints of British soldiers on the walls and having to endure a cookout with something called hot dogs as the main course, as well as their amazement at witnessing the evidence of FDR’s late-night escapades.

Nonetheless the relations between the two nations do benefit, because Franklin and George—the stuttering young man from “The King’s Speech” elevated to the throne by his older brother’s abdication—hit it off, in what’s certainly the picture’s best sequence, a post-dinner drinking session where FDR sizes up the king’s insecurities and offers him some near-fatherly support. It’s really the sole time in the movie that Murray really takes hold of his role, showing the president’s determination as well as his wiliness, and West plays against him nicely.

Otherwise, however, “Hyde Park on Hudson” is mostly an opportunity lost, largely due to the fact that the central relationship between Roosevelt and Daisy never takes flight. That’s partially because Murray underplays FDR’s charm, instead emphasizing his frailty, and Linney makes Suckley so drab and uninteresting. That’s not so much the actress’ fault as the character’s, at least as depicted here. But since Nelson has made Daisy the pivotal figure—although the action frequently strays from her—the result is, if not fatal, pretty harmful.

The supporting cast is fine, with West the stand-out even if no one will confuse him with Colin Firth (in Colman’s hands, by contrast, Elizabeth remains largely a caricature of high dudgeon), and the period detail in Simon Bowles’ production design, the art direction of Mark Raggett and Hannah Santeugini, Celia Bobak’s set decoration and Dinah Collin’s costumes is beautifully caught in cinematographer Lol Crawley’s gauzy widecreen images.

But despite FDR’s inability to walk, there’s a pedestrian feel to “Hyde Park on Hudson,” a conceit with comedic potential that’s never realized onscreen.