You might find some useful info on this thread Importing UK car now practically impossible? - #97 by David_M_Matthews
I have brought a car and two vans to FR from UK. None were classic/restoration vehicles but the same formalities may apply, to some extent.
One van was never registered here. I returned it to the UK dealer as a dud and was refunded.
However, on advice so to do I went straight to Douanes when I came ashore at St Malo and paid the import duty.
When I returned it to UK, still a UK reg vehicle, my application for a refund of import duties was turned down because I should have declared it as re-exported first. So watch out for that if you’ve paid but are returning a vehicle to UK/IE