More to the point, where you going in the Alps, and what kind of trails you going to be riding?
Your BFe will be more than capable of riding anything you come across, but will its rider be? I'd suggest if you're going out to Morzine to hit up all the DH tracks, with their massive braking bumps, you want as much suspension as you can get, and even a 5 Spot will leave you gasping for more. If you're going to somewhere with lots of flowing XC trails, and next to no rock gardens or braking bumps, a lightweight XC hardtail would suffice albeit with slightly beefier than UK conditions tyres I'd suggest...
So where (and what trails) you riding?