It is very difficult staying healthy during a ski season...
With everyone living in such close proximity bugs can move very fast through the resort community. The killer gastric flu for some reason always seems to strike just after New Year and is hard to avoid. The best bet is to pace yourself!
However, with all the will in the world, most people get ill sometime during a season. If you've a job with a tour operator you will usually find you have some sort of cover through them. However it can be wise to get your own additional insurance. From a medical point of view you should be okay, but by the time excesses and maximum claims have come into play, if you lose your equipment you'll get very little back. Whatever, you must have some sort of insurance - this link will show you why.
It's also worth checking whether high risk activities such as off-piste, racing and parapenting are included. You're bound to want to do these at some point during the season, so it's worth taking into account. A way round this in France is to buy a 'Carte Neige' or 'Carre Neige' that will cover you for off-piste skiing/boarding. Bear in mind though that a Carte Neige does not usually cover repatriation to the UK, nor some associated hospital costs.
UK nationals should definitely ensure you have a EHIC card which you can apply for online. This allows you to take advantage of the reciprocal health agreements that Britain has with 40 countries over the world (does not include Canada and the USA). The reality is that the EHIC will not cover you for all of your treatment and certainly not bloodwagon or ambulance journeys, however many insurance policies are not valid unless you have this card.