I'm not sure that's a visual effect. Looks more like a moving platform to me.
(And technically it would have been a blue screen in that era. Green didn't arrive until digital compositing; in 1964 they were still using optical printers for visual effects of this sort.)
But however it was made, I agree that it's a weird shot. A YouTube commenter says it "captures the feeling of 'walking on air' as lovers often feel, and allows us to? completely focus on their emotions rather than the physical action". But it just made me focus on the weird physical action.
Thanks for posting this. It's been a few years since I've seen The Umbrellas of Cherbourg, and I'd entirely forgotten that the memorable song in the scene was from that film.