Paying social charges is not what gives you access to the French health service, they are used to pay benefits to people in need. Your access to the health service is through your cotisations to a caisse (if you are working), directly to URSAFF if inactif, or because of your S1 if you receive a UK state pension. And the PUMA (health) system is accessible to anyone who is a resident in France, it is just that there are essentially different ways of paying for it. If you live here you can be part of the health service, so they won’t take your CV away.
We pay social charges on our income despite the fact that we will never be entitled to any benefits from it! (But we don’t pay them on our UK government pension).
If I extrapolate your situation to ours when we arrived here as inactifs, then our right to get a carte vitale was based on stable residence and having an income above the threshold. How that income was earned was not a question. So if you have an adequate unearned income from your investments then what’s the problem?
Tax officers generally know about tax, but don’t know about immigration requirements of access to healthcare so may well be steering you in an odd direction.
I really don’t know how you would get a definitive answer if you have already spoken to tax people. But it just seems odd to me to go to all the fuss of setting up a business when you could just be classed as inactifs who have a healthy unearned income, and pay your taxes & social charges on that income, plus your cotisation to URSAFF for health.
How is your healthcare funded at the moment?
(Edit: it just occurred to me that you may have been advised to set up as an AE so that you pay cotisations and therefore get entitlement to healthcare that way. And that’s why you were told you lose your CV if you stop your business. But you can get access to healthcare in other ways, France wants everyone to be part of the healthservice)