I want to add one thing here--if France doesn't fall in 1940 and thus Hungary remains neutral and avoids being taken over by the Soviet Union, then Horthy might try doing what Franco did in Spain and have Otto von Hapsburg succeed him as head of state after his death. After all, if Franco could restore the Spanish monarchy, why exactly can't Horthy do the same with the Hungarian monarchy?
Because all of its neighbours, except maybe Austria, would be opposed.