In reply to PhilWS:
Skied La Plagne with the kids last year, and will again in a fortnight (7 year old on his third trip, and 4 year old on his first). We have done ESF again because as Babika mentions, they will move them up or down so they don't end up having a horrid week being either out of their depth or bored senseless. That said, their English is not always great (albeit better than my French) which can be a bit of an issue with the little ones. Have heard decent things about Oxygene also.
The danger with ESF if they haven't skied before is they end up in the Piou Piou class. This class is basically sobbing 3 year-olds shuffling around blow up penguins for the day. But at 6 and 7 they will be fine (and as the ESF instructors tend to be young blokes, they will probably think they are ace).