Got a caravan - but not done Europe in it yet.
Get a good one with lots of space in case it rains / pisses on you.
Check if it comes with an awning etc - older canvas ones are f***ing massive when packed - ours fills the car roof box. A newer tent fabric one with lite weight legs will be better space & weight wise.
Both my folks & the in-laws have a campervans, they'd agree the repacking to do day trips is a pain - BUT you can tow a small car, (on a trailer), for the day to day stuff behind motorhomes, see:
There's also a load of free camp sites in France & elsewhwere for motorhomes, (but not caravans), which will allow you a few nites stay in a town - these are maintained by the local council on the assumption you'll spend a bit in the locality. Will check with inlaws re website if needed.
Wasn't one of the MTB teams flogging their old motorhome / support truck??
[Damn can't find the article - but I think it was on bikeradar or something]
Whichever way you go - good luck.