Here's a pretty comprehensive listing for French resorts - Peak Retreats concentrates on resorts only with a good ski history all season. But nothing can guarantee you good snow in April, or any time. Opt for the first week of April 2012, French schools are still in session that week, only us Belgians already on holiday with much of the UK I believe.
www.peakretreats.co.uk/ski/Snow-Records.htm
There are loads of UK travel operators who specialise in Family catered chalets such as Esprit. Ski Familly, Hillwood, Ski Beat etc. We always do self-catering so I don't know all of them, these are just ones I see quoted often here.
Oh one other thing, Switzerland generally offers free ski passes to under 9s, whereas France is it usually under 5s or 6s. That's great, but their ski lessons can be far more expensive, typically Swiss.
As you have non skiers, it does not make sense to go to a place with a huge ski area. As you have 2 young children, the nearer you can get your accommodation to the STARTING POINT of ski school AND lifts accessible to beginners (eg chair lift / bubble and NOT a drag lift) the better really. There's nothing more tiring than walking with your own skis and your children's skis too, even worse when the walk is up hill!!
If you are looking for a pool though, you are fat more likely to get that with French self-catering apartments and hotels than with a catered chalet which is sold to Brits - very few have pools, more expensive ones have saunas and hot tubs.