you dont give the ages, or whether camping, camping car or using hotels. But as suggestion at least for teh french part..
As you are leaving from London, if you take the overnight ferry from portsmouth (about two easy hours from London) to St. Malo it will get you to france fully refreshed early * 8.30) in the following morning. Then follow the route to Rennes, Nantes, Poitiers, Limoge to see the Milau bridge. Between Limoge and Milau there are water parks in both the Lot and Gers river valleys ( kids love water, these really just beaches bythe river, cheap and safe) and if the kids are happy all is well .
From there take the roads to APT via Avignon and pass through the Verdon gorge. This is beautiful, and again there is at least one water park there. From the end of the gorge it is easy to enter Nice and North Italy or Switzerland direct. I would be tempted to follow the rhine for a while ( at least to Strasburg). Then come back through Aachen and work your way to the Belgian coast. ( very good camsite in middle of Mons for tents/campervans) There is then a mostly free Auto route to Caen where you can take a ferry back to portsmouth ( again with Brittany ferries). Brittany ferries not cheap price wise, but you save on overnight accommodation and two days of your holiday by travelling when you are asleep.