There's no connection between The Internationale and The Downfall of Paris.  I'm not sure that there are any words in English (presumably you don't just mean a translation from the French?), unless Shield set any in his opera of 1790 that gave the tune its English title; there may well have been broadside songs set to Ça Ira, of course, but I don't know of any at present; I still have a number of references to look at.  The tune began its life as a dance tune, and returned to that rôle after its revolutionary adventure.  What little information I have so far is here:  South Riding Tune Book: Notes: The Downfall of Paris,  with a couple of useful links.