I would have thought that the answer was pretty obvious. Any engine shut down or major problem on a 2-engine aircraft calls for a landing at the nearest suitable airfield.
Assuming that they were on a southern track and were out of the hills when the problem occured, then Nice, at close to sea level, would be an excellent option.
I cannot believe that anyone in their right mind would head back into the Alps on one engine! Even if they were that stupid, their licences would be pulled before they hit the ground!
I freely admit that I might be out of date having only flown 4-engine aircraft for the last 42 years (apart from 8 years on 3-holers).