...is actually a very well known traditional song in France, that I think almost any kid could sing to you...

Ah, that's neat. I don't know why it's not more popular in the States. I find it a really good song in any language. Meanwhile, a huge amount of people here know Frère Jacques and Alouette.

I was wondering where and when it came from, and that seems to be unclear

That's what I also found, based on a quick search.