In reply to phildawson:
We spent our summers out in Chamonix when we were teenagers, on a shoestring budget
top money saving tips
Cycle it's only about a 4 day ride (even for the epicly unfit) from Le Havre to Chamonix even loaded with climbing gear and you will have access to a load of good areas without having to walk, or pay for busses
walk up don't take cable cars (you will be fit)
eat load of pasta and bread (i still can't face pasta 20 year later!)
find a good campsite, there are a few small cheap campsites scattered about, most are not on the internet (check in to one you find online for a few days have a wander around town near the hospital and south towards servois to see what you can find)
If you have a trade and speak schoolboy level french you can pick up casual work on chalet renovations, (knocking on doors and asking has worked for me)