The medieval song says on the bridge (“sur”) but the bridge was too narrow to dance in circles so the dancing was likely done on an island under the bridge (“sous”).
Sur le pont d'Avignon
l'on y danse, l'on y danse.
Sur le pont d'Avignon
l'on y danse tous en rond.
Les beaux messieurs font comme ça,
et puis encore comme ça.
On the bridge of Avignon
they are dancing, they are dancing.
On the bridge of Avignon
all dance in circles there.
The fine gentlemen bow like this,
and then again bow like this.