If the filer can prove that they speak French and have knowledge of French culture, they can gain French citizenship. It might require taking a few classes, but the most difficult hurdle (having lived there (legally?) for over five years) has been passed.

It'll take them more effort, but after living in France for long enough to lose UK voting rights I should hope that the rest of the citizenship requirements should be easy.

This assumes the filer wants French citizenship, obviously: if they want to stick with permanent residence but still want to vote then there's no solution, you can't have it both ways.

With 15 years of residence, I believe they're eligible to apply immediately. They'll just need to pass the language test and the culture/history test. Get the background checks and the other processes done.

They are likely not legally allowed to remain in France at the present time. They do not have French citizenship, nor a residency permit, since none was required while they had EU citizenship. This will complicate (though perhaps not bar) any citizenship application.