I would be surprised if the inhabitants of any country have welcomed occupation by foreign troops, especially if they were obliged to billet them and feed them. Even when they are allies theyare likely to be seen as 'over-paid, over-sexed and over here"; when they are conquerors, and military rule is being imposed there are going to be serious resentments.
Foreign troops may be welcomed when they are seen to be driving out another oppressor - Prussia in 1813, Holland in 1814 - but the relationship usually sours pretty quickly.
The French must have been serioulsy unpopular in Prussia for the people to have welcomed the Russians, yet Marshal Macdonald reported that was happening in Januray 1813.

You've got to look at what was actually happening, not how the system would have worked in 'ideal' circumstances - ie everyone doing what Napoleon told them.

regards,

Susan