The British bought property in France without problems before the EEC came into being and when we leave the EU we will still be able to do so in France either for a permanent residence or a holiday home.
We will most likely be subject to the same regulations as Australian and American buyers, and they buy without problems.
For us there may be a little more 'red tape' when buying but nothing too onerous.
If a mortgage is required, we will not be able to get, as French nationals can, a 100 % mortgage and the maximum is likely to be around 60% for non EU residents.
Until the terms of our leaving the EU are confirmed we will not know what the implications will be for taxation. For example, at the moment there is a dual tax treaty avoiding double taxation. There may be different rules for social and local taxes.
If permanent residency is planned we have yet to establish how healthcare will be handled. For the transition period the existing rules will apply., but after it will probably be necessary to have private health insurance
The EU has said that British nationals will be able to visit the Schengen area for 90 days out of 180 days without having to apply for a Schengen visa. (This will of course include France).
It will be necessary to complete an online ETIAS (European Travel Information and Authorization System) application from 2021 onwards. (Presumably similar to the Amecican ESTAS)
If you are planning to derive an income from your French home, the tax implications have yet to be ascertained.
As you can see, there are several important points to bear in mind, and doubtless they will be agreed in the course of time, but nothing to prevent you buying a lovely property in France.