Although I have a doubt or two that mstrang@provide.net is still logging on daily and waiting for an answer, it's a good question.

Wiki gives at: Clicky

The song was originally composed by the 16th century composer Pierre Certon, though with a very different melody to its present version and under the more accurate title of "Sus (sic) le Pont d'Avignon". The modern version only dates from the mid-19th century, when Adolphe Adam included it in an 1853 operetta entitled l'Auberge Pleine. It was popularised by an 1876 operetta which renamed the song, inaccurately, "Sur le Pont d'Avignon."

According to the article people used to dance under, not on it.