I think it's a realistic budget, especially if you’re prepared to organise yourself, rather than a package, and would consider self-drive/self-catering. You'd probably be looking at £1k for accommodation: dh and I have paid this for a 1 bed apartment in a well-known French resort in mid-March - there are bunk beds in the hall and a sofa bed in the living room as well - sleeps 6; there's a decent kitchen with an oven and dishwasher, and it's less than a 1 min walk to the lifts/ski school meeting point. A couple of years ago the same apartment cost us £400, so prices have rocketed recently. Look at agencies in the resort - I've found these cheaper than AirBnB which charge a service charge and cleaning fee which bumps up the price. Apartments are often family owned, so furniture may be a bit eclectic, but they are usually warm and comfortable, even if the decor is not particularly modern. 1k for lift passes - you may not need these for the first day or two as a lot of resorts have free lifts on the nursery slopes: also depends on the size of resort you go to. Some resorts will do a family or tribe lift pass that works out cheaper. An agency will often give you a discount on lift passes.
Driving would require tunnel, fuel, tolls, an overnight stop both ways - Novotel/Ibis/Ibis Styles is a good option, close to motorways and do family rooms, often with breakfast included - and parking in resort. You'd need a set of snow chains as well (and practice fitting beforehand) and knowledge of driving in icy conditions. Roads are usually cleared very quickly if it snows, but better to be prepared. Ski/boot/helmet hire is probably £100 each and lessons maybe £200-250 each if you're looking at 5 or 6 days in ski school. Lunch can be in your apartment - doesn't have to be on the slopes - it's an opportunity to take off your boots and relax for a bit before hitting the slopes in the afternoon - and an excuse to check out the boulangeries in resort (ditto breakfast). Driving allows you to shop on the way to the mountain so you don't pay inflated prices in the resort. Having said that, my experience is that resort supermarkets have deli counters where you can buy a meal to chuck in the oven, so you can keep cooking to a minimum. We used to take some pre-cooked meals in a freezer bag for the first few nights as well. An apartment gives you your own space and freedom to do what you want: you can go out to eat if the budget stretches, but it's nice to stay in and relax with a glass of wine at the end of the day and chill in your pyjamas
. We always take a few games and download a few films to watch in the evenings. That still leaves a fair bit of your budget to spend as you see fit. Try and borrow as much gear as you can - Decathlon is a good place to start if you need to buy any.
Ultimately , it depends what your budget and expectations are. For some, a ski holiday is all about the catered chalet experience, but that comes at a price. We were never able to stretch to that, so have always skied in the way described above. Completely understand that it wouldn't suit everyone but, at the end of the day, the slopes and the snow and the sun are the same, regardless of how much you spent on your holiday 