Here's an excerpt from Tem42's Jan 15 2003 post to that thread:
"There are a number of children's rhymes based around this melody; for more information about the melody and it's original lyric, see "Streets Of Cairo". This writeup, on the other hand, will be devoted to the modern mutations of this tune as preformed by the children of America (and probably other countries, too). These various versions of the song are often adapted as clapping rhymes and jump rope rhymes.
First of all, it should be noted that since the seventies, France has more and more frequently been replaced with Mars. I don't know why this is, but it seems to fit in well with the song's drift into nonsense. I won't try to put the various lyrics I've found in chronological order, but I will start with the older 'France' version, and 'progress' to the 'Mars' version"
-snip-
Tem42 then posts a number of examples of these rhymes. Some of his {her?} risque, and/or "politically incorrect" examples aren't included in this Mudcat thread.