Of course this is not the only way to enter the French SS system. There are several routes, andyou have to follow the correct route for your set of circumstances.
If you are living legally in France, in receipt of a UK pension and no entitlement to a French pension, then an S1 would be the correct route for you.
Assuming you are a UK passport holder then resumably you have had private health insurance in France up to now because it is very unlikely that you would have been able to obtain / renew a residence permit without showing proof of healthcare.
Why did you not join the sécu system as soon as you moved to France? You seem to be making this far more complicated for yourself than need be. Moving countries is nota problem as long as you do it properly and make a clean break with the country you are leaving. It is making half a move and trying to keep your finger in two pies, so that you end up not fully complying with any one country’s rules, that makes things confusing and can land you in a mess…