Oh, I don't know, the little bit that 2 popes who dared to disagree with King Philip were murdered and replaced by a succession of puppets installed by Philip and de Negorat (and their successors) might be a little FACT that you (and the church) conveniently choose to ignore.
At what point did the election of Popes get turned over to the Cathars? I want to see that Papal Bull. For the Cathars surely installed at least Clement V, and likely his next four successors.
The "Roman Pontiffs" never resided in Avignon, only pretenders put in place by secular rulers of the French kingdom, who used them to advance their Earthly ambitions. To suggest otherwise is to ignore history. Thus the reference, Avignon Captivity.
Clement V and his successors were legitimately elected by the Cardinals in conclave. See Phillip Schaff's History of the Christian Church here.
If you have historical proof otherwise, I'd like to see it.