Should I start a an EURL or EIRL business in France?

I have been self employed in France since 2009. I was originally registered as réel simplifié. Since I was new in France with limited French I struggled to understand the accountant so I switched on the 31/12/10 and here lies the problem. I have been since that date, registered with company house in the UK and have my accounts done in France and pay French tax only. My paperwork is then translated into English by another company I pay for who then submit the details to Company House after they have translated them into English. I pay no UK tax just French.

It appears since 31/12/10 I have had no right to a carte vitale and the case was closed even though I have continued to pay my Hamony mutuelle which is obviously of no use without a card. Would my accountant not of picked this up? Where am I covered for health care as I don’t pay into the UK either. Does it need backdating and paying and if so how much will it cost as its 4 years?

As you can imagine this is a pickle so I have decided that I need to change back to just a French registered company once again. My accountant has suggested an EURL (Entreprise Unipersonnelle à Responsabilité Limitée) but I was told it is in the accountants benefit as there is plenty of accounts to do. I was then told by an English accountant that my business would favour a EIRL. I hope you can help a very confused man with no healthcare and perhaps this is why I have received no help with re entree and child benefits for my children here in France.