“Hyde Park on Hudson” director Roger Michell, center, is fascinated by Americans’ fascination with British royalty.

Eighty-three years before Kate and William announced their impending spawn, Americans were just as obsessed with the British monarchy. We fought a war or two to establish that anyone could come here from anywhere and be anything, all the while looking across the pond, almost envying a world where being born to the right family was very nearly all that mattered.

“The royal family is a fairy story,” says Roger Michell, the British director of “Hyde Park on Hudson,” out Friday. “And it has more potency in a country that doesn’t have that particular fairy story. It’s more powerful, it’s more mythical.”

Nominally, “Hyde Park” is a fictionalization of a visit King George VI (the guy “The King’s Speech” was about, here played by Samuel West) made to FDR’s New York estate in 1939, intent on securing American help for the impending war with Germany and Italy. The film focuses on the class and cultural differences that swirl around the king and queen, FDR and Eleanor, and FDR’s distant cousin Daisy (Laura Linney), with whom FDR is having an affair.

George, unpopular at home, has to convince Americans he’s a good ol’ boy while maintaining that aura of cool mystery Americans associate with the British monarchy (a tricky balance, and one that’s largely tied to the eating of a hot dog).

“It’s such an odd thing that Americans have this extraordinary fascination and affection for British royalty,” Michell says. “And yet … in a way, the film is telling the story of a president who’s trying to democratize a king.”

On a smaller scale, the two focal marriages echo the theme that sometimes people have to navigate unsteady relationships for the greater good. For the Roosevelts, it was “a marriage where his early infidelities and betrayals grew into this remarkably affectionate and loving relationship,” Michell says. “That’s a huge success story.” As for the king and queen, Elizabeth has to deal with her promotion from minor royal to major figurehead. “This was thrust upon her. This wasn’t her idea of a good time,” Michell says. “So the film shows their relationship as being not unhappy, but certainly not without difficulty.”

It’s in those personal moments that the film finds its greatest success, leading up to the climactic, frankfurter-centric scene.

“This whole film is predicated on a sausage,” Michell says. “The king biting a sausage, in a tiny way, changes the whole world.”