Caravanning in Europe is very enjoyable - as someone else said, go for it.
Also as stated, fuel in France is always cheapest at the huge supermarkets (which are great fun in their own right!) such as Carrefour, Auchan, and (the cheapest at the moment) L'Eclerc. Most of them have two 'sides', one for credit card payment at the pump (French banks only) or the other side for all other payments including UK cards (debit and credit.) If your 'van is long you may have to choose with care, but anything up to a 'normal' 14 footer or so, you will get through - with care. However when leaving the pump don't turn before your van is out of the 'slot' or you will likely take a chunk or two out of the sidewall of your offside 'van tyre as the islands usually have a stainless steel trim that sticks out a bit further than the masonry.
Most French motorways (autoroutes) are very smooth and often fairly empty, but it will cost you around 12c/Km when towing so costs can rise rapidly. Look at www.autoroutes.fr before your go and it will work out a route for a caravan without going on chargeable motorways (there are a few free ones.) If the sign is blue and says 'peage' it is chargeable - if you go the wrong way there is always an escape route before the entry gates.
As for sites, all cities and large towns, and many smaller towns have a municipal site which can be guaranteed to be clean, quite well appointed (i.e. mains at every pitch) and inexpensive. Beware though that your standard 25m UK mains cable may well be too short - carry two to put in series, plus a BS5750 socket/Schuko adapter as few continental sites (particularly France) have blue outlets. Also make a blue plug/socket tail with the L and N reversed as (in my experience) the vast majority are reverse wired. Supply current varies from 16A, through 10A down to 6A and even 3A, so choose your appliances with care.
As for places: France but not far try Le Touquet with its fantastic beaches or the end of the penninsula around Caen. If you want to go further Paris is always a good place, and there are good municipals at Angers, Samur, Tours, Bourges, Troyes and Rhiems. Alsasce-Lorraine is worth a visit albeit a long way - 1500 castles alone - and a good base is the superb municipal at Obernai. You can also cross the Rhine into Germany.
Belgium and Luxembourg should not be overlooked although they don't have the hypermarkets of the French: the municipal at Ghent (Blaarmeersen)about 90 miles from Dunkerque is very pleasant and Ghent has more to offer than Brugges (and some say Brussels,) the Ardennes in SE Belgium is very green with much forestation, and Luxembourg is worth a visit - especially as it has the cheapest fuel in western Europe by a margin!
Even though Holland probably has more caravanners than most of Europe, their sites are generally not set up to take tourers and few speak English although much of the population does. Germany sites are always well equipped but are few and far between.
Hope that helps - a bit?
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