Hi, I’m here in France working as a cross border worker (employed). If you are are a x-border worker then UK will be responsible for your health ‘cover’ in France. I’m having issues getting HMRC to send the form and did a bit of extra research around it which I posted - hope it’s of help on the health side. It is quite tricky filling in the application form - they read mine wrong the first time and thought my pattern of commute was working in UK Mon-Fri and [working] in France weekends. Cross border health cover arrangements are continuing post transition period as part of the Trade agreement so you are eligible. I suspect you will have to set out carefully which country(ies) you are working in. If you are thought to do work in both, HMRC will write to ask France to decide which country is responsible for your health cover. The requirement to commute is currently suspended up to June at the moment . Anyway I hope that’s of help - or sorry if it’s adding to confusion. Obviously, being company directors you aren’t exactly in my situation as an ‘ordinary’ employee. I am aware thought at you can register a France ‘office’ and yourselves as employees easily enough if you have under 20 (?) staff.
Regards. PS this is my first attempt at pasting a link from one post to another so following instinct here…