Here at Compass we have been in the business and involved with buyers of all nationalities, and particularly Brits, for a good number of years. I had to obtain a 'carte de séjour' (residence permit) when I first arrived and set up my own business (I still have it somewhere...). There are no restrictions in France on who can buy a property. For British people living or moving to France in the future there is likely to be some sort of permit requirement but that is not the object of this article.
Not so long ago, and certainly well within our recent memory, any non-residents selling a second home in France had to appoint a fiscal representative ('représentant fiscal') upon sale of property for the purposes of calculating and ensuring payment of capital gains tax (CGT) - 'Impôt sur la Plus-Value'). This was the case even where there was no gain... This obligation applied to British people too when their individual interest in a property exceeded 150,000 Euros. This meant that it was not the notaire who handled the purchase who looked after this aspect but usually a company with specific accreditation to do this (naturally for a fee...).
Then things changed and the appointment of a fiscal representative for residents within the EEA (European Economic Area) was no longer required so for the last few years this has not been an issue for many individual sellers (rather than companies). Evidently, come March 2019 this could well become 'a thing' again.
So if you are selling, or thinking about selling, your second home and live in the UK be aware that shortly the rules could well change back. If you wish to prepare yourself then have a look on-line and inform yourself about companies that offer this service (and their fees) so that you are ready if need be. Most importantly, make sure that you get your original invoices, details of the firms and proof of payment prepared for major work that you have done. In our experience the fiscal representative firms are very strict about what they will allow as offsetable against the liability (one of the main reasons being that their financial liability is engaged if the tax authorities decide that the seller owes more than has been declared).
One of the firms, SARF, has produced a leaflet in English with some further details that you can find easily on-line. Here is an extract about who is affected by this requirement: