The first time we camped as a family, we slept on a cheap inflatable mattress with normal bedding, no chairs, a small table, single burner stove and not much else! I would recommend you at least get chairs. The lack of kit was also because we had a tiny car and couldn't fit much in! Go to Decathlon and GoOutdoors as they both have good, cheap deals on.
We sail with DFDS as they're generally much cheaper but book as soon as you can.
We usually go to municiple campsites and find them either from recommendation or www.camping-municipal.org/. They're not all singing and dancing, but they are usually well maintained and have access to the town swimming pool. Also look on UK Campsite as they cover France too.
The other option would be somewhere like Domain des Forge. We stayed in one of their eco lodges in 2012 and it was about 900euros for 2 weeks so would save the cost of tent and equipment.
My DCs last year were 4.5 and 1.5. The 4.5 made friends on the first day and was quite happy hanging around with them at the playground and on his bike.
For things to do, we look on the local websites and good old Rough Guide from the library. And of course once we've decided on the area I stick a message on Mumsnet.
Good luck! I love holiday planning!