It doesn't always work out cheaper to go for a few days (which you will probably have to organise yourself) compared to a week long package deal at the last minute, because you can often get good last minute deals on the package holidays if they have a room or two they need to fill. However if you can go midweek you might get a hotel with a room free, especially as we're well into March now and away from school hols.
If looking at France, and organising yourself, search French websites for hotels, they are cheaper and better than the British run places in my experience. Fire off a bunch of emails to them and await response, I've done this and found somewhere eventually. Also in places like Chamonix there are climbers hostels (bunk accomodation) which are cheap and cheerful and might have spaces midweek).
Group lessons are normally based around the weekly trade so might not work out for you - another option would be to organise a one day one on one lesson, not cheap but might be the best way to get going. Are you boarding or skiing, the learning curve is different (skiing probably easier to get into at first).
But basically, go for it, I was amazed how much fun it was first time I went.