And to answer the question: The bits you most likely would like to backup is your profile data, right? Like with many linnux programs, your own settings and profile data is kept in a hidden folder / file in your home directory. When it comes to firefox, the .mozilla directory in your home directory is the one youre looking for.
The actual program usually is scattered around /usr/* But it rarely makes sense to backup those anyways as they dont change. (Well, with firefox, they actually do, so you might want to backup something like /usr/lib/firefox or simiar, I have no idea where mandriva keeps it, but slack has it under /usr/lib/firefox-<version>/ )