Quick allied victory ? Depends who are the allies. Anglo-French or Anglo-French-Soviets ?
If they include USSR, in joint USSR-Anglo-French invasion of Germany in 1939., there is a possibility that they "liberate" Poland and whole of eastern Germany. USSR keeps anexed territories, Poland gains Danzig, but the rest of the east Germany becomes DDR. If not invaded by USSR Slovakia, Hungary, Romania remain autotarian nations dependent on Antante aid. This means Czech republic gains indipendence from Germany, maybe even Austria.
Maybe Hitler kills himself, maybe generals shoot him and try to do separate peace with Anglo-French allies.
Maybe his high ranking subordinates ditch (suicide, killed by USSR or Wermacht) Hitler and Himmler leaving Hess, Goering, Goebels, Heydrich etc. in charge ready to work with Antante in fighting against USSR (Goebels dream scenario). Maybe they just keep rump West Germany (OTL UK and USA sectors).
With Germany not occupied and denazified, France most likely decides to annex/permanently occupy Rheinland west bank.
There most certainly are no international trials, because there are no mass crimes of Final solution or Generaplan Ost, making germans just agressors and treaty violators in average european dictatorship of that time. Without USA there is no one to force nor Germans, neither other allies.
It is very doubtfull that Antante would be able to force denazification and democratisation policies without total defeat of Germany.