We can't restore european monarchies because the social class that formed its backbone has mostly disappeared and the ones left are horrifically degenerate. "Fascist dictatorship" is a terrible form of government that leads to mismanagement and catastrophe. A complex system of checks and balances similar to the US constitution will probably be needed.

I think this isn't that big of an issue though, as the reconquest of Europe is naturally going to lead to the emergence of a new legitimate ruling class. The form of government will have to be designed pragmatically and we still can't know what the circumnstances will be. The most important thing by far is to ensure long-term legitimacy and stability.