How many of them were common opportunists and how many were really convinced about Nazi ideology?
You didn't have to be a die hard Nazi or even a friend of Nazi Germany. Installing a puppet regime like Vichy France was enough to keep the population under control for a long time. Even after a German withdrawal, the threat of a repeat invasion would have been sufficient to keep these regimes in line (i.e., acting in the German interest) in my opinion. And don't forget there were other fascist nations in Europe at that time. Franco for example survived until the mid 1970's, which shows that I am probably right with my assumption about long term population control.
In all history of mankind you will never find two democratic states that went to war with one another!
Funny though that two nations which are proud to belong to the group of very old democracies are also responsible for most of the wars that were fought in the past three centuries. Not to mention that these two "defenders of freedom and democracy" are also guilty of committing some of the worst atrocities in history. What I'm saying is that claiming to be a democracy or republic doesn't mean much if you are not living up to your own standards. You can still show some pretty sh*tty behavior.