We have a couple of options for President.
Depending on the route that Alfred-Georges Gressent (Georges Valois) went in this timeline, he could either be a member of the AF (highly likely considering their popularity ITTL) or a Syndicalist intellectual. However, unless he's dead, I think that the best candidate for president would be Jean Juares, who started as a Radical and then became the leader of the moderate Social Democratic faction which combined with the revolutionaries to form the SFIO).
Now, we need to ask ourselves what planks such a coalition would have. But to ask which planks we would have we need to first ask what France's problems are. To me our biggest threat is international revolutionism, of both the Monarchist/Fascist and Bolshevik blends. I think that we can weaken these Revolutionary movements by satisfying the Real demands they are asking for--namely (in the case of the Bolsheviks) a more equitable and democratic society. To this end, I can see 3 main planks the coalition could build itself around--
-Antimilitarism (Which is not a relatively difficult proposition--we can weaken international Bolshevism by supporting Social Democratic movements in other countries--a question; who is in charge of Germany right now? If its the SPD is in charge we can move for some sort of treaty with them, or better yet, an alliance. But in the case of less developed countries [Poland, Spain, Yugoslavia], if we created some sort of Social Democratic Internationale with the aim of educating foreign social democrats, we could weaken the strength of international Communism).
-Greater Democracy within France (some sort of representation for workers communes, as well as a decentralization of authority, giving more power to local governments?)
-Direct funding for government-controlled infrastructure and heavy industries, and accepting the unionization of the public sector.