I'm surprised that Reelya neglected to expand on
industrial unionism, the concept that all Syndicalists run on, regardless of their other beliefs. Syndicalists (IF I RECALL CORRECTLY) more on the anarchist side tend to support it as a means of cooperation between syndicates and collectives, whereas the more state-oriented socialists support it as a replacement of liberal democracy, having a union structured of representatives directly elected from the workers of affiliated industries.
I think you should probably read up on the literature of those affiliated if you want to know more for yourself and more about the differences within the movement, but I'm afraid I can't recommend much, as it's not something I delve into very often. The only title I can remember off the top of my head is 'On Anarcho-Syndicalism' by Rudolf Rocker. I also am not a syndicalist, or even very socialistic for that matter, so I'm probably not the best person to be commenting on this.
As for Kaiserreich, I am pretty sure the French military is meant to be central government conscripts and militias formed by political radicals. Play Darkest Hour's version of Kaiserreich for a better explanation of pretty much everything in the mod.
Sorelians are
also very interesting, and I can't summarize much of it. Georges Sorel had some influences on Fascism, if I'm not mistaken. Reflections on Violence influenced, one way or another, the philosphy of both sides of the spectrum.