As others have mentioned, the French School Holiday Period (typically 4 weeks total) is busy, with the Paris holiday weeks the most crowded. Am guessing the OP's group might have kids in Paris schools...
La Plagne might be another option. It is one of the most visited in the world with good reason-
large domain that connects with Les Arcs (Paradiski)
Terrain for all levels- lots of easier terrain on the La Plagne side and out of Les Arcs 1800, but with true expert terrain (North Face of the Bellcote glazier for true off piste as well as some "natural: aka ungroomed, "on piste" terrain out of Les Arcs 2000
Train service from Paris
Might be somewhat less expensive than places like Espace Killy or 3 Vallees BUT expect to pay higher lodging prices everywhere during this time period
Good snow reliability (but never guaranteed anywhere)
A variety of villages to choose from (where you stay in a particular resort does make a difference, so research this also)
Espace Killy, 3 Vallees & Avoriaz/Port du Soleil are also great places to consider. Personally, I wouldn't consider Chamonix for your group. Chamonix has some great skiing, but the different resorts are not as well connected as Paradiski, Espece Killy or 3 Vallees. While in town accommodation might be cheaper in Cham, it will likely mean taking a bus to different resorts (with not everyone preferring the same area). While I think ski in/out or short walk in/out is always best with families, if budget considerations make this difficult, I would consider someplace like Bourg St. Maurice, walking distance to the funicular that goes directly to Les Arc 1600. There is ski rental/storage right at the base of the funicular as well as in 1600, so this makes the schlep easier.
Wherever you decide, I'd book early- this includes lodging, train, rentals,ski school, off piste guides, restaurant reservations etc. as the Paris school holiday period is the busiest time of the season for all French resorts.
I'd cross post (or do a search) on Snowheads.com- lots more former European skiers (aka British) there who have vacationed extensively in the French Alps.