There is a french film I saw last year in an arts movie theater depicting an American man and a French woman, supposedly married, but we're never sure, not even at the end.

They go to a museum in France and discuss whether the "Mona Lisa" is merely an imitation, or the real thing. This is the question that goes through your mind about the couple as well. Are they married or playing the game of a married couple.

I can't remember the name, but I'm anxious to know because I just read "The Real Thing" by Henry James, and it's certainly a similar plot.