Can I live in France and trade via a UK registered business?

I run a UK private limited company owner and director. I spend most of my time in Antibes, France - where I service businesses and yachts IT requirements. Let me start by giving some information on my current circumstances:

• UK limited business director (since 2012).
• I am the only employee.
• I use a UK registered company to service my UK clients.
• Turnover of around £100,000 per year.
• I am currently taking the minimum wage allowed to keep taxes low, and this allows me to take dividends from the company each year.
• Currently single, but I am getting married this month, to my French registered fiancée.
• UK registered address.
• All business, regardless of where it is carried out (France, Italy, and UK) is accounted for in the UK and this is where I also pay tax
• I am not a registered French citizen.

With the above in mind, I would like to eventually become a registered French citizen and even open a business here if possible. In an ideal world, I would like to become a French registered citizen and still run everything through the UK business. My thoughts therefore are that I keep the UK Company and bill UK clients from this, and then have a French company for the businesses and yachts I manage here.

1. Can you give me any tips or pointers regarding the best type of business scheme for my requirements?
2. Regarding accounting, how would this work? For example, do I have to declare any French profits to the UK Company and to HMRC and vice versa for the French system.
3. Can I continue on a similar scheme in France (pay a low wage and gather dividends at the end of the year)?