If you're resident in France (183 days?) you'll be taxable in France, but there's a form to fill in to avoid double taxation. It's quite simple to declare your earnings from lodgers and another form for overseas earnings.

Excellent. Thanks.

The French definition of resident is here. http://droit-finances.commentcamarch...t-non-resident

The UK definition is not the same, so the two may overlap. Then HMRC and the fisc have to decide between them. But of course you can influence the decision by arranging your working pattern so that it matches, or doesn't match, certain criteria. No doubt your advisor will advise you.