When did French central authority collapse?

Okay, I know at some point during the late Carolingians / early Capetian eras in France, central authority collapsed and the king had virtually no power outside of Paris. But when exactly did this happen? During the reign of any specific kings? Was it during the Carolingians or the Capets? And is there any POD (as late as possible, ALAP) to avoid this decentralization?
Probably during the last few Carolingians is when it started, as the dukes got more freedom. Then the Capets came and that put the nails in the coffin, because the Capets had even less authority outside of their domain, the Duchy of Francia (or Neustria).

So to avoid it, I'd say prevent Hugh Capet from taking the throne, have a Carolingian survival, with stronger kings. If they can curb the independence of the dukes and centralize enough, that would solve the problem, centuries early.