Starring Alicia Vikander and Mads Mikkelsen. In Danish with English subtitles. Rating not available.

A Royal Affair, a handsome enough 18th-century period piece, can’t quite shake the perfumed odour of having settled for so much less than was possible.

Directed by Nikolaj Arcel (who helped adapt the film from a Danish novel portentously titled Princess of Blood ), the wig-happy effort has a lot to say but gives almost everything the same coat of Masterpiece Theatre gloss—outlined by a syrupy orchestral score—so the results are soporific even if many elements intrigue.

The chief problem is the failure to take more than circumstantial interest in its main subject, Princess Caroline Mathilde of Great Britain, played with fetchingly blond solemnity by Alicia Vikander. Our aristocratic protagonist is married at age 15 to a cousin, Denmark’s Christian VII (the scene-stealing Mikkel Boe Følsgaard), a prancing kinglet who turns out to be even loonier than her brother, Mad King George III—a pretty significant parallel that the movie doesn’t bother to reference. Caroline’s youth and sheltered background make her a slow starter in the convoluted game of Danish politics, which is filled with local reactionaries who, perhaps not coincidentally, resemble Tea Party Republicans.

On a basic storytelling level, more effort could have been put into the young queen’s supposedly transformative chemistry with Johann Friedrich Struensee, a German physician who touts Enlightenment ideals and can handle Christian’s nuttier moments. (He’s played by the reliably compelling Mads Mikkelsen.) These two foreigners eventually combine forces to bring out the king’s better angels. But shy, frilly Caroline doesn’t get more interesting. Reportedly both homely and outspoken in real life, the actual queen was into cross-dressing and racing her white stallion through the streets of Copenhagen—just one (or two) of many missed opportunities in this forgettable Affair.