Originally Posted by Robot Arm
It's been years since I've seen it, but could it have been Until the End of the World
(Which is, technically, not set in the future anymore.)
You beat me to the answer. My husband and I both deeply love that movie. We saw it in the theater when it originally played and own the laserdisc. There's supposed to be an extended DVD but we haven't seen it. It was, in our minds, a worthy followup to the beautiful Wings of Desire
by Wim Wenders.
Set at the end of 1999, William Hurt plays Sam Farber, the son of a scientist who lives in a commune in the Australian outback. Farber's mother is going blind, and Farber's father is working on a machine that will allow her to see recordings inside her head. Farber is going around the world recording messages from all of her friends and relatives so she'll always be able to access not only their voices but their images too. He meets up with Claire Tourneur (played by Solveig Dommartin, RIP), a woman who is lazily traveling around to punish her cheating boyfriend (Sam Neill). Farber is having to travel under a different name, and be mysterious, so that word of this machine doesn't get out. She meets him, loses him, finds him, loses him, finds him and finally travels to Australia with him to meet his parents. The scene in the OP comes from one of her efforts to try and track him down again.
There's a LOT more to it, but it's one of those sloooow, lyrical movies where the journey along the way is, if you have the mindset (and time, and patience), much more important and interesting than the destination. The title comes from the fact that there's a wayward defense satellite (or something like that) that's gone wobbly, will go out of orbit and will fall to the earth, setting off a nuclear explosion, but no one knows exactly when or exactly where, so people are trying to get a lot of living in before it's too late. It's been years since I've seen it and that part of it never interested me. Sam and Claire's travels, and the machine that changes these people's lives, not to mention the most freakingly awesome soundtrack of any movie I've ever seen, is what interests me about the film.