I do now and it's been stuck in my head since you posted O_o

And Bah Bah Black Sheep. I used to sing a verse from each to confuse my children.

Right you are bensen- and as scarmandingo alludes- “bah bah blacksheep” is also a variant.
The melody behind these songs has been used at least a few times in history and at its youngest dates to the 1740’s or so- the French folk song “Ah! vous dirai-je, maman“ is said to be the origin of the melody- but the first time the melody appeared in notation I am aware of was when Mozart created his 13 variations of the song and wrote them down. Mozart tends to be a popular guy through his time into the modern age, so of course the melody would catch on anywhere one might be exposed even second hand to his influence, independent of proximity to France or French folk culture.
Twinkle twinkle little star started out as a poem and at some point (I’m it aware when) it was set to the melody we know today and that caught on. Fun stuff.

12 variations* typo.

lol. That was awesome. Thank you.