NoMommsen is correct regarding the lack of enthusiasm for the war at this stage. Hitler's personality peaked after the fall of France, but when the war began and the western powers sent their declaration of war, people did not rush to the flag with enthusiasm. They went about their duties, but nonetheless.
It is pertinent to note that the prospect of attacking France disconcerted many Wehrmacht generals. Even a hardline Hitler loyalist like Reichenau, who would be enthusiastic about war crimes during Operation Barbarossa, was unhappy about it and may have even leaked German invasion plans to the Dutch. It's quite possible that Führer Göring, unsure of his position, goes along with a more conservative operational plan devised by the OKH instead of Manstein's, if he attempts an invasion, though he will doubtlessly try to get a negotiated settlement first to get out of a war he was not happy about. How that works out is another question.
At this stage Göring's prestige has not been damaged by the Battle of Britain, Stalingrad and so on yet, though his role in the Blomberg-Fritsch crisis has not been forgotten by the army. I think it's likely he'd be able to become Führer/president/chancellor after the bomb goes off...but whether he stays it is another question. He would not be able to count on the obedience of the army or the party the way Hitler could.
Assumig the bomb achieves maximum impact, then a good chunk of the Nazi party elite has been killed or incapacitated (of course, this is up to whoever writes a timeline). This leaves largely second string figures, which is convenient for Göring because they cannot mount an effective challenge to his succession, but also leaves him more vulnerable to any possible coup if the army goes for it. We should take care not to treat the Heer as a monolith that was just waiting to pounce though. Halder conspired, but then got cold feet and Brauchitsch was the exact opposite of decisive. Oster and his buddies wanted to coup and eliminate Hitler during the Sudeten crisis, but they were a particularly radical group.
