According to this Swedish source, they are about to start the climb to camp 9, which was their last camp before heading for the summit.
The picture is taken at camp 8, at the South Col, which is at about 8000 meters. The previous summit attempt by Evans and Bourdillon failed, so Hillary and Tenzing wanted to set a higher camp and try to get to the summit from there.
Gaston Rébuffat was actually an instructor at a military school of mountaineering run by the 27th mountain infantry. In any case, the French government clearly appreciated his contribution to history because it awarded him the Légion d’honneur in 1984.