It was a single shot, hand loaded weapon. They hollowed out the propeller shaft and put the gun there, with the loading mechanism extending back through the engine to appear in the cockpit.
As for why he did it? Propbably just because he could. Fonck is noted for his using a single burst from his machine gun of around 5 rounds to kill his opponent. He almost never got in dogfights, he would fly off alone and high above the battlefield, spot his target from “impossible distances” as his comrades put it, and then kill them. So honestly, he probably only used the 37mm because he could. Frances other leading ace, Georges Guynemer, whom everyone liked more than Fonck, was the first to use the 37mm in his place (The French army as a whole made massive use of portable, one shot 37mms, that famous picture of American troops prone in a burning forest during the offensive has them loading a French 37mm) and was able to down two German plans with it.