Set up a business in UK and France?

I have been running a corporate video production company in the UK for the last 18 years but have decided to move to France to be nearer my aging parents who have been in France for 26 years. I have had a house near them for 7 years (as a second home) but plan to move there permanently and rent out my house in the UK (I am single with no children).

I had planned on keeping my business in the UK and managing it from France by employing freelancers in the UK but I understand that the french system will assume I have a satellite office in France and will charge me about 55% in social charges on the profit I might earn from the company in the UK - I think this would make it very hard for me to keep it running so I feel I need to think of alternatives.

I am interested in the auto-entrepreneur scheme with a view to setting up a photographic business (selling prints and cards at markets and in shops, at the same time as offering my services as a portrait photographer in a home studio) Could I also be a freelance producer working for french production companies under this scheme?

Can you clarify which category the auto-entrepreneur scheme would put me under? If you have any views on any other business structures that would suit my situation and would allow me to keep & benefit from my UK company I would very much appreciate your thoughts. Also, is there any such thing as joint residency between France and the UK as I am not sure where I would have to say I am resident?