It is desirable to fix exactly when Hitler dies. I am assuming that your intention is that he dies between the start of the attack on Norway and the fall of France. The first question is who takes over. The later Hitler dies, the better it is for Goering. The Luftwaffe was very successful in both campaigns and I suspect that that would make Goering almost certain to be accepted from late May. The only obvious significant change in the military operations from 10th May to 25th June might involve the famous halt order before Dunkirk. However, it is not at all obvious who did what and whether the panzers could have reached Dunkirk. In fact there must also be butterfly effects but we cannot predict them. So let's assume that we reach 25th June 1940 more or less as OTL but with Goering in charge (although not so firmly in charge). What happens next?
A major problem is that we need to understand Hermann Goering. The popular view is that he was lazy, stupid and addicted to drugs. Maybe. It is also possible that OTL he realised that he was always going to be kept as Hitler's servant and lost some desire to push for his visions. Perhaps taking power would have given him the energy to try to change the world according to his ideas rather than Hitler's. Unfortunately, it is hard to guess exactly what he would have tried to achieve. He might have been biased towards military operations against Britain rather than against the USSR because the Luftwaffe would be the main instrument used against Britain. He might also have been less keen to gamble on a quick victory against the USSR than Hitler as few people in history have gambled more than Hitler. Another question is whether he could have talked more convincingly to American newsmen. Hitler's word was not widely accepted by 1940, so could honest Hermann have presented the gentler face of Nazism?
Finally, in the probable event that Germany loses its war, we can be certain that there will be many saying that Hitler would have done it all so much better.