The main character (Davos Hanich) is a prisoner in the aftermath of the Third World War, in a destroyed, post-apocalyptic Paris where survivors live underground in the Palais de Chaillot galleries.
Scientists research time travel, hoping to send test subjects to different time periods "to call past and future to the rescue of the present".
They have difficulty finding subjects who can mentally withstand the shock of time travel, but eventually settle upon the prisoner, whose key to the past is a vague but obsessive childhood memory of a woman (Hélène Chatelain) during an incident where a man was killed on the boarding platform ('the jetty') at Orly Airport.
"12 Monkeys" was based on this film. I haven't seen "La Jetée" since just before I was in high school. As we used to say back in the day, "It blew my Mind",..still does.
I've been looking for it since that noisy, gleeful time. It just occurred to me that "La Jetée" might be on you-tube,...of course it was. So here it is.
Btw I could launch into a righteous rant about how Hollywood takes fantastic French films, and remakes them into stupid American ones. However I'll lay off for now. Watch the film see what you think.