So I am thinking that Poincare takes emergency powers and rules as Prime Minister until the legislative elections in November. He will likely be slightly more ambitious and stubborn in taking more from Germany, especially opposing a fixed sum for reparations. His inclusion is likely to stall the passage of the Treaty of Versailles for anywhere from two weeks to a month or so. Could he win more from Germany?
The other major butterfly is that in OTL Clemenceau, sensing that the general strike being readied for May 1, 1919 could lead to a communist/anarchist attacks or even a putsch, gave all French workers the eight-hour day in return for them calling it off. This move largely did stop the general strike. ITTL, I doubt Poincare would make the same move.
The French general strike starts up on May 1, 1919, and I predict it to run much like the railway workers' strike of January-May 1920 in France, but worse. The government will decide to oppose the strikers, of course, but will they be able to break the strike? I believe things will get ugly: another anarchist attack, perhaps, like the bombings in the USA. And with the public scared of anarchists... The French might use very heavy-handed tactics to break the general strike, and its going to radicalize the workers a bit more than OTL. We could definitely see a more unified, stronger transformation of the Socialists into the Communists in France, which is pretty scary. As for elections in November, I could see the socialists being the most affected by the strike: I could see them losing more, due to negative opinion against the violent strikers earlier in the year, or winning more, with more people inspired that a change needs to happen. I believe they'll likely do worse, which won't mean a thing other than there will be more of an initiative to radicalize and transform the SFIO into the French Communist Party.
Clemenceau's assassination could very well lay the seeds for a Communist revolution in France...