In reply to tingle:
BASS in Chamonix provide first class instruction.
Good private lessons and inexpensive are incompatible. BASS range between about £170 for 2 hours to £400 for a full day. This becomes much more affordable if you organise into groups of 2 or 3 of a similar standard.
If you are there outside peak season (school holidays) I seem to remember that ESF are cheaper for private lessons, but with them it is much more of a lottery as to quality and fun and charm