I would not think of the Downfall of Paris tune as I know it when I listen to the Edith Piaf recording. Or this recording (also with a set of lyrics in the notes)
https://www.youtube.com/watch?v=-srLjMRjoVI

or this instrumental by the Yorkshire regiment

There is just a bit of similarity at the beginning of the tune. To me, I am not speaking of the same air when I say Ca Ira as when I say or play The Downfall of Paris.

Downfall of Paris, Irish dance tune https://www.youtube.com/watch?v=vuljlIwx638played by the Davey Triplets (lol)