Maria, good to mention that. My wife and I spoke to RSI, RAM, URSSAF, etc, and there is no problem if everything is invoiced, receipted and so on as AEs should do. We have both mainly worked for a single source of payment albeit the actual tasks are different and for various end users, none of which shows in bookkeeping. If it is simply a lump sum paid into an account every month then they will not let it go on for too long. The tip to put in at least one other piece of work for somebody else as the minimum 'other' is good for getting round that.
Yes, of course you can. In fact, if the company does not want you on its books this is the best possibility you have.