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. At first you think they just met and then in a french restaurant there is a switch and you realize they might be lovers playing the roles of married people. I just saw it last year

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.