Indeed 
Well, the fixpencil falls under that category that many people in France and Switzerland call a Critérium. It’s one of those names belonging to a specific product that eventually becomes the name of the thing regardless of their brand, like “Gillette”.
I know a bit of the history of these pencils because I’ve always been a fool for them. They were based on a original design by Caran d’Ache — which technically makes them all fixpencils! — but in France just before WW2 a pencil maker called Fabrique Gilbert modernised those models by introducing an “embrayage” system (French for car clutch), where you’d press the cap and the lead pipe had a step and a spring and the jaws went out to free the lead and expand and block the lead when they retract… so maybe what we now call the “clutch” is actually the name of the Fabrique Gilbert system?
During the first half of the 20th century and until the 70s, other factories in France were making these models too: Blanzy Pouré (they were making those nice raw aluminium ones, Conté (they made shorter models and also wonderful 5.6mm artist pencils) and later also BIC which I believe merged with all of them and is now the owner of that specific name Critérium which you see in supermarkets and etc.
I’m guessing this pencil is probably an off-spring from one of those factories. Maybe a test model? The lead pipe is notoriously different from the common fixpencil and “criterium” models, which I think makes it more interesting. The clutch doesn’t come out, it’s trapped inside with the spring but it all comes together nicely when you put the pipe in again. The body is lacquered aluminium (like the fixpencils and unlike the criteriums which were either from raw aluminium or plastic resin), the clip has some delicate bends and the pushbutton is truly truly nice in all its grooved glory with a sharpener inside and probably made of nickel (idk for sure…).
Really a nice piece. And according to the previous owner, quite rare.
When you compare it to all the other criteriums and fixpencils you realise there is a deliberate attempt of refinement of the very simple parts they were usually made of — so who knows, maybe this was an attempt to make a more expensive model? or a one-off? 