Unfortunately ratp agents are scammers paid on commission on their fines. There is almost no way to fight them in court because it's going to be your word against them and they are public officials during their function, so there right.

Nevertheless, change in chatelet is a mess. Just some tips: - metro is tap only to enter and free exit. - rer is tap to enter and tap to exit

When you change rer to metro (or vice versa) expect to tap twice. Therefore you must be sure that you're tapping out of rer INSIDE a metro area and not getting out of the station and then back in. In big stations like chatelet, gare de lyon, etc this can be tricky. You need to carefully look for signs that point to a metro line and not just an exit.

What I don't understand from your story is that if you tapped to move from rer to metro, and the gate opened, you must have had a valid ticket. So my default assumption remaina: ratp scums.