Hi Northern. I've stayed in Le Praz many times so some information below that hopefully will be helpful.
The three valleys big selling point is that it is the biggest linked ski area in the world, generally it is regarded as a place for people who want to do a high mileage on piste rather than as a classic off piste destination. All pistes are marked out by poles and most people without a guide largely stick to them. Having said that the 3V does have off piste opportunities and a reasonable selection of black runs - try a search on the Grand Couloir in Courchevel.
Le Praz had a big new chairlift which went for this season, so you can be quickly into the slopes and usually you can ski back to the village for most of the season, you will find most of the lifts across the entire three valleys area are modern and fast. Le Praz is in the Courchevel Valley, Meribel is the central valley and Val Thorens is the third valley across. Typically good skiers would expect to cover most of the area during a week's stay. From Le Praz across to Val Thorens is about an hour and a half for reasonably fast skiers on piste, and there is now a fourth valley with a couple of lifts beyond the Val Thorens valley. The drive from Le Praz to Val Thorens means going back down into the valley, along and then up the Val Thorens valley - most people would just ski there for the day. If you wanted a slightly quicker start a drive round to Meribel from Le Praz is quite quick if the road is open and it would save you a bit of time but personally I wouldn't bother.
Not sure whether you will find it easy to rent Avi equipment - whenever I have doen it the guide provided the equipment. Typically to go off piste in the Alps if you aren't qualified or know the local area in detail most people hire a guide / instructor, if you are off the marked pistes it is at your own risk and as was said above it is not protected - 1 person has died so far this season above La Tania which is just around the hill from Le Praz. The local ESF (French Ski School as you speak French) will have guides or you can try independent schools such as http://www.skinewgen.com/ In addition, with the freeze thaw cycle in March if the weather warms up a guide can hopefully find decent snow off piste - if it hasn't snowed for a while it may not be worthwhile going off piste. Important to check your insurance as well, typically insurance policies in Europe don't cover off piste unless you are with a qualified guide - evacuation can be expensive if you have an accident and aren't covered. There is off piste all over but some of the highest is off the Cime de Caron and La Masse in the Val Thorens valley.
You will find a three valleys thread on http://snowheads.com/ .
If you post there you may be able to get recommendations for individual guides, and information on Chamonix - although that is a long drive and you would probably want to be sure the Vallee Blanche was in good condition before going and the weather was going to be conducive. An alternative would be Val d'Isere which is another classic resort and more renowned for its lift served off piste opportunities than the 3V - its about a 1 hour drive from Le Praz.