In France there is CNIL (https://www.cnil.fr/) and they seem to try to follow-up on reports, at least for french located companies/websites I think.

I filled 2 years ago a few complaints. It took over 1 year for an answer. Basically nothing happened.

The Data Protection Authority are underfunded and understaffed. They try the best with their resources.

Can't we fund these authorities with the fines they generate?

Not the best way, I know, but better than nothing.

That would create a perverse incentive inevitably leading to corruption.

It creates an incentive (to identify entities breaking the law), but I don't see how this is perverse. It's the desired result.

The same reason funding police departments on ticket revenues is bad. It incentives overzealous enforcement, where it's not so much about preventing people from breaking the law, but instead figuring out what you can pin on them.

I would say this is quite a different situation:

Police enforcement includes the police powers of arrest and detention.

GDPR enforcement is (I believe) limited to a fine which can be appealed to a court. If the enforcement department turns out to be wasting court time, then there are likely to be significantly negative consequences for that department (at least, more than for the police in the US).

I agree that fine collection is not an ideal way of funding a department, but not all incentives are perverse just because they exist - incentives are allowed to align.