It’s awards season, and you know what that means: overproduced costume dramas about the flaws and foibles of historical kings and queens. Or, to paraphrase the gossip weeklies, “Royals — they’re just like us!”

“A Royal Affair,” Denmark’s official submission for this year’s foreign language Oscar, is one of the stodgier entries in the parade, but it’s also one of the more straightforwardly enjoyable: a crowned-heads soap opera that balances effectively between pomp and melodramatic circumstance. In the bargain, it tells a startling real-life story of queenly bed-hopping, Enlightenment ideals, and Cabinet coups in the name of the people.