Typically, the mudguard hole would have been drilled "vertically" on the rear stay bridge at this period, at least for French mudguards, if indeed it was intended to have mudguards to begin with.
Bowden cable operated brakes only came in the picture around the very late 1910 or for the most part in 1920s. They were to my knowledge always attached to the forks or rear stays - like an optional extra. A flip-flop rear hub would have been the norm, with potentially one rear brake.
When you stripped it, did you notice any witness marks on the forks the brake had moved lower? Potentially it may have had 700B wheels.
It's a great find this is. If only it could talk