As someone in German Government who has written a thesis on OSS in government:
Happens regularly, on a small scale, but almost always eventually leads to a rollback to Windows. People are discontent with the solutions on Linux since they have to get used to something else, and the aging governmental workers and exactly very keen on things changing.
The City of Munich had a similar program of switching to Linux before, only took Microsoft to open an office in the city to revert on those plans.
The federal government recently finished rolling out a centralised, unified client around all of their ministries and other institutions. Which OS? Guessed it, Windows 10.
Dont get me wrong, having something like the French Police would be amazing, but the highly federal nature and old workforce of government make it super unlikely for Linux to have a proper chance. Taking into consideration the lack of suitable employees to drive forward such a change, the lack of money at local government levels and the fact that most of the specific software required doesn't have a version for Linux doesn't fill me with hope.