Re registering for tax - the reason people are mentioning this is simply because under French law, every resident must declare income to the fisc annually, regardless of whether or not that results in you paying any tax. It’s a legal obligation, everybody has to do it. Droits et devoirs and all that.
Re disguised employment, the main criterion is the level of supervision. If you’re given a result to deliver and it’s up to you how you achieve the deliverables - the methods and materials you use, the timescale - that is normally s/e. If you are told what, when and how to do the work, ie carrying out an employer’s instructions, that is employment. There are other criteria but mainly they stem from the supervision one - can you subcontract all or part of the work; can you turn a job down; if you make a cockup, do you absorb the loss or are your earnings unaffected and you employer bears the loss; is your business financially dependent on the employer/client ie if they went into liquidation tomorrow, would you still be in business; do you market your business, do you bid for work, do you set your fees and issue invoices or does your employer offer you a salary and give you payslips, are you in charge of the strategic direction, can you decide to change the focus of your activities, etc etc etc. Essentially France doesn’t have a “freelance” category, a self employed person is simply a person running a business that employs only him (or her), and it’s fairly obvious, really, whether a person is running a business and all the cr4p that comes with it - keeping accounts, budgeting, maybe investing, thinking of ways to become more profitable - or whether they’re working for their employer’s business and letting him worry about all that.
But the main one is the relationship between worker and client/employer - level of supervision versus degree of independence, and from what you’ve said, I would say you could be unquestionably self employed… Some people will tell you you can’t be self employed if you have only one client but that’s an urban myth - it would be unusual but possible, just as having two or more ‘clients’ doesn’t automatically make you s/e - all of some of them might be classed as part time employers.
I think the confusion was that in your first post it sounded as if your employers were going to put you on the payroll:
It would be better if you invoiced them per job. A monthly fee is in effect a salary, and that’s what it will look like to your bank, because no genuine business achieve exactly the same turnover same month after month after month. Why not simply agree a fee per project, and if they’re long projects invoice in several stages if you want? After all part of running a business in France is knowing how to set your fees and charge for your services.