You're right about the 6 months thing - strictly speaking, but in practice people do drive un-reregistered for a year and beyond - one of the reasons being that you get a lot of students and others who are here for a year or two and so don't bother.
So it depends how much life you think the car has left in it. You can sell it (maybe) to the local Cass for spares, or strip it and sell the spares yourself, and then get the remains of the carcass taken away (for which you'll have to pay), or you could use it to chop in against a brand new French car for which you'll get a favourable discount for taking an old car of the roads - that's how I disposed of my RHD Polo, or you could hand it over to the local Lycee Pro if you're feeling generous for kids to tinker about with.
You do have a number of options therefore. 's up to you.