Depending on who and where you hunt you're likely to be limited to about 200m max range by the guide.
When I did it 10 years ago in the Haute Alps with the French the drill was like this.
1. Are you fit?
2. Walk from the base of the mountain up through the foothills and then onto and up the mountain.
3. See chamois peering down at us as we walked up in plain view. They look like gargoyles peering down from the roof a cathedral
4. Lots of glassing
5. Choose chamois that fits what's allowed (age, sex etc) and what you can afford (size)
6. Walk closer in plain view until you start to reach the sort of range that the chamois appreciates it's in danger
7. Stalk/move into dead ground
8. Peer around cover, guide give approximate cost
9. Ask guide if it's safe to shoot as the Chamois is standing on a rocky outcrop with only air behind it.
10 'It is safe eez only mountains'
11. Aim at center of chest - nothing clever like just behind shoulder as unknown wind across valley might shift bullet
12. Curse light rifle as heartbeat causes cross hairs to jump
13. Bang - chamois rears, drops, much congratulations.
14. Walk across to Chamois
15. An hour later, 200m descent, 3km around valley, 300m uphill arrive at Chamois
16. Much congratulations, photos etc
17. Gralloch chamois, load into rucksac a) congratulate yourself on being wise and hiring a porter or b) curse and start the journey back
FWIW a nice slippery bullet that opens fast zeroed no more than about 200-225m and a simple scope all of which you know well and can shoot under some pressure. I wouldn't go too light and I certainly wouldn't drag clicks etc around. 7x64 is an excellent choice - you can get ammo in sports shops in France.
Have fun - it's the most memorable stalking I've done.