The World, the Flesh and the Devil (1959), The Quiet Earth (1985), Z for Zachariah (2015, adapted from a 1974 novel). 

Three variations on a same theme: in a post-apocalyptic world, a guy meets a girl, and they are apparently the last survivors on Earth, and a second guy appears.

The 50′s film has a  good reputation, I liked The Quiet Earth (a long time ago), Z for Zachariah seems potentially interesting.