but we kept meeting each other at each turn."  
At one point in this work, a woman asks the protagonist for his name, and he replies that "it doesn't matter."  They subsequently meet in a garden inhabited by frozen people in suits, then meet again in a drawing room where a card game is frozen, where the woman comments that "you never seemed to be waiting for me but we kept meeting each other at each turn."  Ending with one character losing herself completely in leaving the titular place with the protagonist, it is based on The Invention of Morel by Adolfo Bioy Casares. This film begins with X asking A if she remembers the affair they may or may not have had at some time and place, but she does not, and they are interrupted by M, a man who might be A's husband.  Starring Delphine Seyreg, this is, FTP which dreamlike French New Wave film written by Alain Robes- Grillet and directed by Alain Resnais, whose protagonist claims to have seen his lover previously in the gardens of Frederiksbad?
At one point in this work, a woman asks the protagonist for his name, and he replies that "it doesn't matter."  
{Last Year at Marienbad} or L'{année dernière à Marienbad}