Bear in mind that plenty of people do drive to go skiing so it's very doable provided you take sensible precautions. We always drive to Tignes which is in the same area. Not sure where your starting point will be in France - we go from Calais - but it's easy motorway driving to Albertville and then dual carriageway most of the rest of the way. Might be worth getting a toll tag so you can go through the fast lane at the peages. The road from Moutiers to Aime is not very nice in the rain; if you encounter snow it's more likely to be from Aime onwards up to the resort, although we've had bad weather from well before Chambery in the past.
We always drive through France on a Friday so the roads are quieter and stop overnight somewhere like Chambery. From there, it's about 1.5-2 hours to get to Tignes the following morning before the roads get busy. They can get horrendous in the French holiday season which is why we go early.
We always go at Easter - I can't comment on Feb half term - some years we've needed to fit chains (usually just for the last few miles), other times have been fine, clear weather and roads; I think we've used them once in the past 5 years. Regardless of whether you go in Feb or April, you will need to take chains in the event they are needed (gendarmes patrol the mountain roads in bad weather and will make you pull over to fit them; if you don't have any, they will make you go back down the mountain to buy some) and will need to be familiar with fitting them. You don't want to be faced with fitting them for the first time in a howling blizzard! If it does snow you will find the roads are cleared very quickly (though you may still need chains), but make sure you drive slowly and keep in a high gear; you will see the locals driving like nutters, just ignore them and let them overtake. We make sure we have a snow shovel in the car (never used it, except for making snow holes in the resort!) a thin pair of gloves to protect fingers when fitting chains, something waterproof to kneel on when fitting them, and a cloth/kitchen roll as your hands can get v grubby.
We really enjoy the journey - its a part of the holiday for me, I honestly wouldn't want to do it any other way, so please don't be terrified. Do book a covered parking space in the resort if you can. It will cost, but means your car will be snow free at the end of the week.