A Place for Lovers (1968)
A Place for Lovers is a 1968 romantic film directed by Vittorio De Sica and based on the play Gli Amanti by Brunello Rondi and Renaldo Cabieri. It stars Faye Dunaway as a terminally ill American fashion designer in Venice, Italy who has a whirlwind affair with a race car driver (played by Marcello Mastroianni).
More at Wikipedia.