Dual citizenship

Which second nationality you want to apply for?
It's the best to contact the embassy for further assistance and guidance.

I am a British citizen (Scottish) but would like to know if I could have dual French/British citizenship. before U.K. leaves the E.U?

According to my knowledge it takes two years before the exit is final and I don't see how this can affect the application for a dual citizenship.

Again,  contact the embassy.

Thank you and I will see what I can find out from the Embassy.

I looked at this a few years ago Bob - but be prepared for it to be a costly exercise. I worked out that it was going to cost me in the region of £500. The requirement from the French side is that all relevant documents (birth certificate, marriage certificate, divorce papers etc etc) had to be translated by sworn translators. They also needed to see the originals (not copies) of all documents.
I wanted dual nationality as I've lived here permanently for almost 10 years and pay tax in the UK and here (directly and indirectly) and so I thought I should have a vote in the matter. In the end, I decided that £500 was too much to pay.
I suspect your wish for dual nationality is inspired by last week's events. You might want to read this advice before going down the dual nationality route.
By the way, England hasn't taken us out of Europe.. The UK had a referendum which resulted in a victory for Leave - but I suspect many in govt are sitting on their hands first to consider the way ahead. No-one has triggered Article 50 of the Lisbon Treaty yet.. and I don't see that happening for a while. As a Brexit is seen by many in the EU as undesirable (apart from the usual suspects) I can see a situation where wiser heads prevail. I think the UK could return to Brussels - armed with a Leave vote - to discuss with the elected heads of the EU a statesmanlike way of moving forward that would take into account the UK's concerns. I think there's growing recognition around the EU that the move to an "ever-closer union" is a step too far for many. I don't think Frau Merkel would like to see the UK leave, however much this would please the likes of the unelected Juncker, Schulz and others - and Frau Merkel's voice carries much weight. From a practical perspective, I believe there are elections in Germany next year and it would do her domestic case no good at all if German products were to be hit with UK import taxes.   
Good luck!   
Pip