So no troop mutiny? Okay.
Well, the mutinies were not violent (eg they didn't kill their officers Russia-style), and I think the Third Republic longevity was owed largely to the fact that no-one had a better or more popular alternative. I don't think that anyone would right after the war, though the possibility of a left-wing coup and a Commune is a definite possibility.
I think I'm leaning towards France to be a left-leaning authoritarian state. A really nasty strain of Socialism that combines nationalist sentiment and state control of industry (maybe even some anti-Semitism). You could call it National Socialism, but that would be lazy.
With the chaos and lost economic opportunity in France, plus the German annexations (which would probably come with the loss in '18), then I think that you're going to see a lot of settlers moving to Algeria. I'm not sure what the population of the place was at that time, but with France's Colonial Empire so emasculated (as presumably it would be by Germany) is it possible that Algeria would be brought more directly into France? Perhaps the socialist government in Paris decides that Arabs can be good Frenchmen (the need to more manpower for the next round with Germany is going to force them to get creative, and this seems logical from the standpoint of simply counting warm bodies who could potentially be put in uniform).
So, this is Italy, with concentration camps. Fascism, then.
A Republican sentiment seems very odd; particularly as it was Imperial Germany that was the victor.
I'm thinking that the feeling will be linked to anti-German sentiments. The royal family was very tied to German royal families (was in fact a German royal family, Coburg-Saxe-Gotha, before they became Windsors in '17) by marriage and ancestory. I'm thinking the British could go towards a kind of anti-monarchial corporatism, led by the Labour Party.
Concentration Camps may have been going to far. I think I'm starting to go more toward a sort of France in Algeria post-WWII kind of model, where the British troops in Ireland basically wipe the IRA out, and then decide the civilian leadership is not sufficently supportive of their cause, so decide to replace the government. Or a peace could be made, and that sets off the coup attempt. The troops would have a rather large amount of stabbed-in-the-back feeling to pull upon, and probably have support from more conservative elements in Britain (since Britain is also gripped by worker unrest). The reaction to the coup could be republicanism if the King gives backing to the coup-plotters (or if Prince Edward does). A coup attempt, followed by a short civil war, followed by the Republic of Great Britain being declared?
This stuff was all done in the 1920s, when the same people that were in the Imperial Army were in the Weimar military. It shows that they'd be willing to hold their noses and work for a Bolsheveik state, and therefore your argument seems surprising.
I think it's possible they intervene; I just don't find it probable.
Intervening would have seemed relatively straightforward though. You give the Russians some guns that you now have from demobilization, help the Whites take St. Petersburg, and then let them fight it out from there. You release POWs to the White forces. I think that this would give the Whites a fighting chance and even if the Bolsheviks are not totally defeated, it will certainly make Russia continue its bloody civil war, which can only be a good thing for exhausted Germany.
But the behavior of the Freikorps is post-Versailles, and therefore out of bounds since the political condition will not exist ATL.
I am a hypocrite and you caught me. I hope you'll find it in your heart to one day forgive me.
My point was that the Germans were willing to commit atrocities in the name of anti-Communism on the home front, they would probably be willing to commit atrocities in a foreign country fighting for the same thing.
The Germans cooperation with the Russians was an alliance of convience. If they could have wiped the Bolsheviks out, then they would have. OTL both were pariah states in 1920. ATL Germany is the winner, and Russia the pariah, the weak, communist pariah. I don't think much of its chances.