The official nomenclature assigned by the RFC was actually 'Fighter Mark 1', but in operations the factory designation F.E.2b was still used, or it was just referred to as the 'Fetubi', or more affectionately as the 'Fee' (as previously mentioned).

The earlier F.E.1 and F.E.2 were different aircraft than the F.E.2a, the latter being conceived at Farnborough as a dedicated fighting design, or "Gun Carrier".

The lines and designations are blurred somewhat, but "Fighting Experimental" is generally used:

http://www.raf.mod.uk/rafwaddington/fe2.html

Copterdrvr, either designation would probably be acceptable, even on the earlier and distinctly 'Farman-like' F.E.2 model, at the time of its rebuilding in 1913 "it appears that some of the Factory's staff believed that the F.E. designation stood for 'Fighting' rather than 'Farman' and planned accordingly".

Hey, if the Royal Aircraft Factory and the RFC/RAF weren't exactly sure as to when and what "F.E." actually denoted, then either is probably 'historically correct'.

The Fee was used as a fighter in it's earliest service history, and then relegated to home defense and nocturnal duty as it became obsolete for daytime operations over the Western Front.

Including the Fee in Knights Of The Sky (ETA still unknown), does add an interesting aircraft to the plane mix!