If you have lived in France for five years or more you can apply to become a French citizen. Unlike the permanent residence card, which you are entitled to, citizenship is in the gift of the French authorities. You will need to show that you are well integrated into French life – including speaking passable French.
If you can get French nationality you would become an EU citizen and continue enjoying freedom of movement to live and work throughout the EU after Britain leaves. French nationality may particularly be worth considering if you are currently in a job open only to EU citizens or if you are, and want to continue being, or plan to become, a municipal councillor. French citizenship also gives you the right to vote in national elections. British citizens are allowed dual nationality so you would not have to give up your British citizenship.
To apply for French nationality – naturalisation – you must be over 18 and have been living in France for at least five years. You cannot apply if you have a serious criminal record. You will also need to sit a language test and demonstrate a knowledge of French history and culture as well as the rights and responsibilities of French citizens. Applications are made through the prefecture although you should be able to get the necessary forms, as well as a list of documents you will need to produce, from your mairie. The application fee is 55€ and you will need to include the usual birth certificate, marriage certificate, passport, proof of continuous residence, proof of address, photographs etc. in your application dossier. Those over 60 do not have to produce a language certificate/diploma but will have their proficiency tested in conversation with state officials.
Once you have submitted your dossier, your application is considered by various governmental departments including the police, mayor’s office and prefecture and you may also be interviewed by the police. The whole process can take up to two years.
NB: if your children were born in France and have lived here since they were 11 they can claim French citizenship on their 16th birthday and will be be granted full citizenship at 18.
Find more details about language requirements here: http://www.ciep.fr/delf-dalf
There are 4 DELF levels (Diplôme de la langue francaise): A1, A2, B1, B2, and two advanced DALF levels: C1 and C2. You need a minimum B1 for citizenship.
You can take a test to determine your level at http://www.ciep.fr/tcf and practice here: http://apprendre.
There are books to help you train for the DELF and DALF exams on Amazon.
The Livret de Citoyen (in French) tells you all you need to know about French history and culture before applying for citizenship. Download it here.