The Glass Fortress, also a French s-f short film, is made in a very similar style:
There is also a 2013 remake of La Jetée made by Matt Lambert:
Then there is Año Uña by Jonás Cuarón (son of Alfonso):
Año Uña is a wonderful film. Stylistically influenced by Chris
Marker’s La Jetée, Jonás Cuarón’s debut film is a ...
Can't be answered for sure but in both movies (La Jette and 12 Monkeys) the body is present in the future. Although the details aren't clear, looks like the psychological aspect is only the beginning of the travel, later followed by the body itself.
I've found several places on the Internet where people claim that Marker could only afford to rent a motion picture camera for one afternoon, and that's why the film has only one moving image in it. However, I can't find any source for that claim that I would consider "reliable" - where I'd say "Yes, that's definitely someone talking from actual knowledge", ...