Hi Check 6,. .Yes it is early days with the State flights and as eyeinthesky said you do block the 2 opposite direction FLs which can greatly increase the controller's/planner's workload (especially between FL320-370) as they have to 'clear the way' so to speak through all the sectors/ACCs on your route.
However, you have the potential advantage of being able to use a high cruising FL where there isn't too much traffic, so dont give up, keep requesting higher!
I have seen many European ACCs and LATCC (as it was)has one of the best Civil/Military working relationships, unfortuneately French Civil ATC dont work/coordinate closely with their Military ATC, a sentiment that probably applies to having to work Non RVSM State A/C in RVSM airspace as well.
So, at the end of the day you've answered your own question "It was only a problem with French ATC !" .