We (2 adults and now 2 kids (7&9 been skiing since they were 3)) have been driving to the Alps (or Andorra) every year for the past 15 years.
We usually assume about £500 for tunnel crossing, tolls and fuel, and we book a pretty cheap apartment £5-600 and cook in most of the nights we are there, but go out a few nights for meals.
Kids Ski school this year is 300€ for both of them and kids ski hire is about 50-60€ each. We have our own kit.
Then you have lift passes, we’re going to Samoens and a 6 day family pass is 775€
I make that about £2300 (ish dependent on exchange rates) which gives you over a grand for pissing up the wall!! Which won’t take long in a French ski resort…
It’s dead easy to drive to places like Samoens or Morzine, 8 hours from Calais. Just remember that Saturdays in February are busy!