smallbusiness.co.uk: Helping your business think big

I would suggest that you if your business will be based in the UK that you register your business with Companies House, which keeps a registrar of all limited companies in the UK. Visit www.companieshouse.gov.uk or call 0870 3333 636 for further information. I would then register a subsidiary company in France. However, I suggest you contact Companies House in the first instance and if still unsure consult a solicitor.