After an hour-long reunion (filmed in real-time except for a few
short cuts), Jesse (Ethan Hawke) and Celine (Julie Delpy) end up in
her appartment. He puts on some music, and she starts dancing
playfully/suggestively (but not overtly sexually), as he sits and
watches her, laughing. She says "Baby, you are going to miss your
plane;" he laughs and says "I know," and the screen fades to
black. The ending is ambiguous in almost every possible way - it's
totally up to the viewer to decide what will happen next, both in
the short and long term.
Thanks, Eytan Z!