Its been a while since I last caved in the Ardeche, but the following caves I recall as potentially being good for kids;
Event de Peyrejal - The resurgence entrance (impressive) can be entered in dry weather and followed a reasonable distance to a sump. As MRO Doc warned however this cave does flood with alarming ease. Also there is an artificial entrance that leads into several km of good stuff (including the best formed phreatic tubes I have ever seen), but it does require tackle for a few short pitches.
Event de Cotpatiere - this is very close to the Peyrejal and apparently is hydrologically connected to it. There is a short climb up to the huge entrance, which had a fixed ladder (iron hoops), handline and a hose (?) hanging down it when I was last there (nearly 15 years ago). The entrance is a huge rift like affair and the massive passage can be followed under a skylight to lots of easy walking until it starts to get wet and muddy. The cave apparently links to the Cocaliere show cave via a gate, but I have never got to the gate. Here are a couple of photos;
Apparently the Goule de Sauvas is also good for a simple "walk in" up to the Grand Marmite. Again it is a part of the Peyrejal hydrological system, but is a sink. The entrance is large, but I have never been inside.
If you happen to be at the bottom of the gorge, you could do worse than visit the Grotte de Midroi. It does have a lake not far from the entrance, about 30m long, and a short climb up at the end of the lake. A boat and ladder would be useful for older kids. There are some fine passages and good decoration to be seen.
Hope this helps...
Ed