The cheapest option for going abroad for me is a Dover to Calais ferry with Irish Ferries, about £150 for the 5 of you. From there you have France, Belgium, Netherlands, Luxembourg and Germany within a few hours drive.
There are SO many companies to book accommodation through it's a matter of going through a few one evening and finding the cheapest option. I've only once found a good with Eurocamp, I've always found them to be extremely expensive but it's a good place to start, you can then check how much it is to book direct if you fall in love with a place.
The cheapest time to go to France is Easter, a lot of France does not have a full school holiday there so there's some excellent deals. I've already booked for Easter and paid 249 EUR for 2 weeks in a one bedroom apartment at a beachside complex with indoor and outdoor pools, gym, sauna, jacuzzi... That special offer ended on Friday though so the same place is now 600! Other deals will come up though, I usually check every so often and grab a deal when I see one.
I search for deals based on price rather than location so my options are always open. If the price is right, that's where we're going!
If you're looking for somewhere with good facilities and within easy reach of Calais, I can recommend Cottages du Valjoly (summerfrance.co.uk) They have lovely little cabins next to the lake, a big pool and other activities that can be paid for, the pool is included in the price. The closest village is called Willies so that always keeps the children amused!