Small French 2-strokes were certainly not used by the British War Department. The pre-June 1940 French Army used Peugeots but these seem to have been mainly 350cc SV Model P107 with later 350cc OHV P115 and P135 models.

The Germans helped themselves to anything with wheels but there wouldn't have been a tactical use for them...Perhaps a depot or dockyard runabout.

Thanks Rik, since a bike this small would have had limited use in the military, I'll just go ahead and do a civilian restoration!