Carte vitale for UK registered business owners?

My brother, our elderly Mother and I came to France in June 2012. We quickly got a Carte Vitale for our mother but have not been able to get one for ourselves as we have a limited company that is registered in the UK and paid our last tax returns there. As I understand it we would need to relocate the business to France but this would mean such large social charges that it would make the business unviable.

The business is unconventional. It is an online publishing company that offers systems and advice for betting on UK and Irish horse racing, therefore I doubt we would be able to set up as an auto-entrepreneur. Last year the company had revenues of £26,000 and my brother and I paid taxes of around £1000 each.

I read this article from which the following excerpt may be useful:

A social charge is also payable on foreign salaries and foreign business income for those based in France, but taxed outside of France. The charge is imposed to cover health insurance in France, so is only payable if you are affiliated to the French social security system in France. It is 5.5% on salaried income, and for business income it is 2.4% up to €34,822, and 9.6% between €34,822 and €174,113 (2013). The charge is also only imposed subject any applicable double taxation treaty.

Would this be applicable to us, and, if so, how would we go about doing it?