Brexit and your situation
Uncertainty continues in the United Kingdom firstly as to the withdrawal date from the EU, the nature of that exit and even whether it will take place at all. As a consequence, the situation remains stressful for British citizens who have connections with France; whether living here, owning a property, having employment or through running a business in the Hexagon. All these possibilities are still facilitated by freedom of movement (fom) and other single market principals all of which for the entirety of the UK, could soon cease all together.
Should the British government manage to pass the withdrawal agreement it signed with the EU 27, fom for UK citizens will stop but within a controlled time-span. If the UK were to withdraw without any agreement, fom rights will cease immediately and UK citizens will be considered as "third country" nationals, and each EU member state will then apply its own sovereign laws concerning that status.
Other arrangements exist through EU conventions etc affecting for example: opening a bank account (residency gives this right), the validity of UK driving licences and car insurance in France and Europe, pet travel etc. However, the French government (and the EU where applicable) still has to determine its policies in many of these areas.
Political positions continue to polarize and fragment in the United Kingdom, from a call for the UK to leave the EU without any agreement what so ever, to the holding of a second referendum, a general election and even a revocation of the article 5 notification.
None of this can really offer comfort.
The first element to retain is the principal of reciprocity. France for example has expressed the intention to treat UK nationals on French territory according to how the UK treats French nationals resident there.
Secondly, the article 50 period has been extended to 31 October 2019 (though this could change to a shorter or longer period), and while the article 50 period continues, UK citizens still enjoy full rights as EU citizens, and it must be noted, the extended time-frame has been of assistance.
Given these two converging factors, it is prudent to act as soon as possible, and British citizens in France are best advised to formalize their situation. The choices come down to applying to acquire French nationality (popularly called French passport) or applying for permanent residency.
It is prudent to take such steps, and since French bureaucracy can be daunting for those not used to its procedures or those who aren't confident with their French, I am offering assistance for those assembling applications for French citizenship (so-called French passport) or for the resident's permit.
For British people working in France, with business concerns in France, or who are trading between the UK and France, I can offer advice as the situation evolves.
I am in close touch with my contacts in the City and we are monitoring the evolution of the legal situation in order to anticipate events. I am specifically following developments as they will affect British citizens with close associations with France (see where I practice), so if or whenever you feel the need to evaluate your situation, do not hesitate to contact me.