“Illee.. Allee…oh” was the lyric I learned in Glasgow tenements 60 years ago -
I am fully resonating with the French theory .. at first when I looked this old children’s thread the needle game song up and saw references to “Alley Alley oh” I thought I’d misremembered. This surprised me as sounds and music are obsessively remembered by me.

I also lived and worked in France and “there in the water” (il y a l’eau) OF COURSE is what we sung as kids. I have pas du doubt