An FIR is established in order to provide a flight information and alerting service. FIRs can and do extend into international airspace. However, within each countries FIR there are rules and regulations for flying your aircraft, whether it's a private or commercial flight, a civil or military irrespective of international airspace.
Incorrect, see
article 3 of the ICAO Convention. Though some would like it changed, see below, but don't hold your breath, EU parliament resolutions are non-binding, non-legislative crowd pleasers.......
Article 3
Civil and state aircraft
a) This Convention shall be applicable only to civil aircraft, and shall not be applicable to state aircraft.
b) Aircraft used in military, customs and police services shall be deemed to be state aircraft........
European Parliament: Motion for a European Parliament resolution on military planes which fly in European air space with their communication systems and transponders switched off and threaten passenger planes