One thing I've always found amusing is how an armoured car is an "automitrailleuse", which can be read as "self-machine-gunning". "Marcheur de combat" is the easiest term to work with, and to go with what the French did historically, I would have them use the same names everyone else does for the vehicle models.
Looking through a few magazines and the web, I noticed that a lot of tank regiments kept older designations, such as the ever so common Régiments de Chasseurs d'Afrique, and most of the reconnaissance groups (like the GRDI and GRCA) stayed unreconstructed for the FFL and the Armée d'Afrique. One case where two types of regiments share the same acronym (like the "Regiment de Chars de Combat" and the "Régiment de Chasseurs à Cheval"), the newer one gets bumped with a higher number (500+ for the tanks). Although I haven't yet come across any French unit using the acronym RMC (Régiment de Marcheurs de Combat).
I can't seem to find any BCC (bataillon de chars de combat) or CACC (compagnie autonome de chars de combat) after 1940, which is sad, because they sound like cool names.