I thought I'd come out of trolling and throw in my 2-cents worth. I'm not in France but I feel strongly enough about a few realities I'd mention a few points and see what your thoughts are.
Someone commented earlier that UK politicians made assurances that UK citizens would continue to have the right to remain in France. No British politician can speak for the EU once separation is complete just as no EU politician can speak for what happens in Manchester.
This projection of 'the other side' is an extension of the mistruths uttered by the Brexiteers.
More recent posts suggest one should not allow knee-jerk reactions govern their response to the vote. However, it seems to me that a second passport (ie. A French one) is 'insurance' against the worst-case scenario. That scenario could be drastic changes unilaterally imposed by the French Government to the criteria used to allow you to apply.
And please, can anybody here honestly say that the French Government only ever yacts reasonably, logically, accountably, and compassionately? Change is blowing in the wind and my feeling is one ought not wait to see how things 'work out' before opting for the insurance. Avoiding the paperwork could be akin to sticking one's head in the sand.
A third point: France currently allows dual citizenship. Until fairly recently, I believe Germany does not. An acquaintance thought about applying for EU citizenship through German heritage but absolutely knew he would have to surrender his Canadian citizenship. If this were the case for France, you'd know it without a shadow of a doubt.
Even if you had to, you could turn over your British passport to the French, wait for formal separation and then reapply for a new one- claiming the original was 'lost'. Unless you formally filed paperwork to renounce your British citizenship with the British Government, you are never not British.
Indeed, all you who live in France stand on that very sharp edge that divides populations into Nation States. The divide between Britain and France is one of the sharpest divides on the globe. Frankly, I'm surprised you aren't all already intimately aware of these distinctions.
No matter. You can hold more than one citizenship. You are no less 'British' if you carry another passport and no less French if you do the same.
I initiated my Irish passport application as my Father was born in NI and the application was received by the embassy in Ottawa on June 16th. I am not counting on my UK passport to access the richness of the continent. It seemed quite straightforward. All in, the process of collecting documents, validating other documents, and paying the fee came to about C$350.00- a small price to pay for keeping one's toe in the game.
The process takes about 6 weeks and I have not heard anything so so far the application continues.
Why am I doing it? Irish rules could change. Who knows. Maybe the EU will impose those changes. That's what 'insurance' is for.
So if you're eligible, I wouldn't wait. No, the sky isn't going to fall- I'm not playing Chicken Little- but why 'wait and see'?
Again- think of it as insurance. If you want to live in an EU country, you really need to have an irrevocable EU document that allows you to do so. After all, you are currently citizens of what soon will be a foreign country. Little or nothing may come of it, this is true. But how do you know for sure?
Should the French government act out of spite and exclude UK citizens requiring you to pack your bags and head back across the channel, crying about it then will be far, far too late.