"Ah, Si Mon Moine Voulait Danser" is a song I didn't realize till recently is a song sung as part of a children's game.    The lyrics seem to be a young woman trying to entice a monk to dance with her, by promising to give him a rosary, a cowl, a sash, a musical instrument, and "many other things." But the chorus has a line about a mill running, and I think the game is connected to that

Here's a very 'rockin' version of As, Si Mon Moine Voulait Danser by Three Days' Grace.