Assuming you do the work in France then the UK Ltd remaining active isn’t really an option - the basic principle would be work here - pay the taxes etc here. I still have a UK company - but I leave France do the project and return - the little bits I do whilst physically in France go through my AE to keep clear water. In some ways I’m tied to a couple of contracts and they like the UK company and the £10 million insurance I have to carry as part of that project would be exorbitant as a French AE- but given I’m project based somewhere in the world it works for me.
HMRC don’t care - its tax for them - its the French who’ll get miffed if they think your working in France and not paying proper taxes here.
A UK Ltd is fine if you own shares and don’t do the work - ie contract it out - or leave France to do the work.
AE is the simple option - there are drawbacks - tax/social charges are on turnover not profit - although in theory the tax/social rates are meant to reflect your expected costs - the other obvious difference you trade as “you” personally - not as a separate legal entity such as the UK Ltd regardless of branding etc…
You can set up a SARL but its a lot more expensive in every respect than a UK company and unlikely to help at your levels of income from the company.
Tax wise - the French declaration is pretty vague - how much PAYE how much “unearned” (Dividends) - no questions about who the employer is so there’s nothing to shout to the French tax man its a bit iffy. But tax wise the advantages of UK companies are slowly vanishing - by the time they’ve hit you in the UK with Dividend tax - the French have taken their cut in Social Charges there’s nothing much in it.
I guess if you want to blag it there’s nothing on the tax form that gives you away - but like speeding its fine until you get caught.
Once resident you have to do a French return - so as before you declare wages and dividends - dividends are treated as “unearned” and social charges are levied - 8-10%'ish I think from memory. wages are looked at as earned so assuming you do the usual wages up to the PAYE limit thats well below tax thresholds - its the dividends that attract social charges.