The movie La jetée is composed from photographs with a voice telling the story. What is the reason he used photographs instead of normal animated pictures? Was his budget too constrained? Or was it some artistic reason?
Is an experimental film. Chris Marker did it that way due to artistic reasons. In the 60's french directors were pushing the boundaries of film as an art, breaking rules to experiment with filmmaking (check Godard's "À bout de souffle" as another example, using non classic montage).
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", as opposed to simply guessing (or passing on something they'd heard elsewhere, with no knowledge of whether it was true). The fact that so many of the sources who make the claim repeat it word-for-word suggests that it's the sort of ben trovato story which spreads like wildfire because it's so appealing, not because it matches the facts.
But whether the story about Marker's financial constraints is true or false, there's a sense in which it's irrelevant. At some point Marker faced a choice; at some point he would have said to himself, even if not consciously, "There may be other films you could make, if only you had a bigger budget, or more time, or better equipment - and maybe you really wish you could make those films, but you can't. The question before you is, do you want to make this film, or not?"
The fact that he went ahead and made the film, means that this was a film he wanted to make.
The most compelling explanation I've yet encountered for why Marker chose to tell the story in this fashion comes from an essay by Landon Palmer on the website "Film School Rejects".
Palmer suggests (I'm simplifying his argument greatly, I'm afraid) that La Jetée is a film about our double-edged relationship with memory: it's the means by which we visit the past, by which we try to glean the meanings we need from that past. But we are so often misled in that pursuit, because we can only revisit short, frozen points in time - what lies between those frozen points is what we imagine lies in those gaps, and our reconstruction may be greatly mistaken.
This, of course, describes not only the experience of the protagonist, visiting the past to try and glean meanings from his all-too-short jumps back in time (which are only possible because of his obsessive memory of the death at the airport), but also the experience of the audience watching the movie, piecing together the narrative from the frozen images on the screen.