The ferries (and Eurotunnel) are definitely your friend here.
Since DD was born in 2013, we have been to France 19 times and have two trips planned next year. This sounds like we're mega loaded, but we're really not you can get some really good value with French holidays and things like Tesco Clubcard points can be used to pay for ferries (P&O/Irish Ferries) and eurotunnel.
It really depends on what you want as a holiday - we've done cottage rental via Gites de France - I mean there are some serious stinkers on there (that look like they haven't been renovated since the 1950s) but with a bit of patience there are some gems on there - we had a lovely one near Colmar in the Alsace, one near Troyes and just outside Nuits St Georges in Burgundy (you might sense a wine-related theme coming up - all doable in a day from the channel ports.
We've stayed with Eurocamp on their campsites and they served us well, but I think their quality offer went downhill in the time we stayed with them. We now use Yelloh Village and Sandaya for our campsites. Cottages are fine, but we have found our kids need more occupying and the activities on a campsite - pool, kids clubs, playgrounds, trampolines etc help you to have time to relax as a parent too.
If you're driving, invest in an Emovis Tag for the autoroute barriers, it automatically registers you going through their toll barriers and means you don't have to worry about someone having easy accessibility to a credit card while you're driving.
In our time we have been via Brittany Ferries - Portsmouth - Cherbourg and then Le-Havre - Portsmouth; Dover - Calais - Dover; Dover - Dunkirque - Dover; Eurotunnel.
We've been NE of Paris (to the same campsite 3 times which makes doing Disneyland Paris doable as a day trip as well), Troyes, Alsace, Burgundy, Loire Valley 4 times, Vendee, Bordeaux, Avignon/Provence and next year we're doing Sarlat/Dordogne. We've also done budget skiing 7 times.
If your kids are preschool, you can still get decent weather in September or June and therefore bargain prices on accommodation. If you have to take school holidays into account, then the last week of August (if you book with a French company like Yelloh Village) is half the price of the rest of summer as the French have usually finished their summer holidays then.
I'm also a self-proclaimed queen of service stations and wee-stops (Google Maps is your friend here) and my husband has the boot packing refined - but please, if you have any questions happy to help!