We have stayed here before castels.co.uk/campsite/br. It still remains one of our favourite ever sites and although we don't like to return to the same sites abroad because there are so many places to try, we can't wait to return. The pitches are great, beautiful bar area with live entertainment every night (giid entertainment not trashy cheapskate stuff), big pitches and a beautiful restaurant belonging to the site but a few minutes walk away so feels like you are really going out! Saumur is a 5min drive away and there is also so much to do in the area.
Don't worry about taking the kids, its really much easier than you think. We drove all the way to the Ardeche this year and ours are 7 and 4yrs old. A couple of cheap dvd players, fully charged tablets, a magazine each plus endless supply of snacks (coolbox on the floor between them plus bag full of crisps and biscuits) and a little stop every few hours really does occupy them. We also play 'count how many caravans you see'!
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Would also recommend the Loire region - Have a look at La Grande Tortue. Great little campsite. We have been there a couple of times and think it would answer all your "would likes". It has a lovely swimming pool with retractable roof etc. it is also near enough to visit some of the Chateau's if you wanted - also close to Blois .
What about Lac d'Orient, (not quite Burgundy, but on the way, near Troyes. This is a very nice campsite on the side of a lake, with pizzeria, and other facilities by the lakeside, and it scores 9 out of 10 on the campsites reviews here. It's been redeveloped over about the last ten years and now has a 'pool complex' with slides, a bar and restaurant on site, good shower and toilet blocks, you can hire barbecues, and buy bread and pastries and basic shopping on site, and there are supermarkets a short drive away. They offer discounted tickets for Nigoland which is a theme park and your children might just be the right age. However, if you like a quieter life then it's not a 'full on' campsite, just a very family orientated one, and should fit your bill - though don't forget all sites have moved on since the days when you used to go with your parents.
The city of Troyes has some nice old buildings, and a lovely mediaeval centre, and there are lakes around with nature reserves if you and/or your children are into nature and natural history.
There are more pictures and reviews on the Eurocamping (not Eurocamp) and if you can go at Spring Bank Holiday (we used to do and found it an ideal time with younger children) then you could take advantage of the ACSI Card rate (17 euros per night) and save 8 or more euros per night on the tariff for a pitch, two adults, car and caravan, electricity, and two children.
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I second Val A’s comments on Lac d’Orient. Even towing you can make it in under the 6 hours as it’s autoroute all the way to Troyes. Also there is good level cycle tracks around the lake. Also has an indoor pool as well as outdoor just in case the weather is a little inclement to still keep the children happy.
Couple of photos added
Lakeside beach across the road from the site
Outside pool area ( taken a few years ago but may be even better now )
Amazing family weekend with old steam engines, classic car displays, market stalls, and full catering and bar. And camping on site - Save £25 by booking in advance.