Or rather, Raimey, I think that Jean Pirlet was an employee of the Mode business, possibly as a condition to the purchase of Pirlet by Mode.
Jean Pirlet signs "pour fonction" i.e. in lieu of the big boss.

M. Dufour of Toulouse likely proposed an "invention" to the Mode house and they politely sent him to a patent attorney.

I used to own a Pirlet sidelock circa 1900 that was Belgian made.
It was my first sidelock that had been badly butchered. I got rid of it in a Parisian auction circa 1990. It would have been fantastic had it not been "restored" by bandits.
The things you have to learn when you start collecting....
Best regards,
WC-