Hi SandDune
As far as I know, you should be OK with one operating FMS in European airspace.
Most European airspace is subject to BRNAV above FL100 which equates to RNP5. if you have this capability, file 'R' on the ATC flight plan (equipment).
In addition, RVSM is active between FL290 and FL410. To fly within RVSM airspace you need two independent altimeter systems, an A/P with alt hold and a mode C txpndr. You also need specific approval form the state of registry, part of which will involve aquiring an RVSM operations manual detailing MEL, equipment requirements and operating procedures, including phraseology. More details at
www.rvsm.com When you have RVSM approval, you can file 'W' in the flight plan.
I should add that all the above is from memory without appropriate manuals, etc., so please crosscheck what I've said. I think that the Jeppesen ATC section has a good explanantion of the requirements.
Hope this helps.