Hi, I'm working on a summary of what happened during the month of February (like a front page recapping the month), but I just made a little something. The composition of the Parlement National, the legislative body of the Fourth Republic, with a tiny description of each party. Feel free to ask questions!
The SFIO, Section Française de l'Internationale Ouvrière, is a Socialist-Communist party. It used to be the champion of the Socialist cause in France, and was briefly in power 1934, but failed to address the colonial crisis that had already brought the Alliance-Union and Radical-Republican governments down. Since then, their support has melted like snow in summer, losing most of their audience and figureheads to the Réformistes. They support a centralized state with a planned economy, on the contrary of the Réformiste decentralized approach.
Réformistes are the governing party. They are the main figures behind the creation of the Chancellerie and the Fourth Republic, and its original founder, Eugène Grindel, is President since the SFIO government fell in 1934. The party is somewhat of a broad coalition, based on former SFIO members, intellectuals and local figures of the left, but also more unexpected figures like Prime Minister Jacqueline Arthuys, who has made no secret of her monarchist feelings in the past. The current policies are oriented towards a decentralized collectivist approach of the economy, seing the workplace as the basic unit of a society. This party generally trends toward a progressive social policy, having granted women equal rights in 1935, criminalized racist offences in 1938 and depenalized homosexuality in 1941, but struggles to find a cohesive answer on some topics due to the sheer size of the movement.
The Parti Chrétien Démocrate is a fairly recent party, born of the Christian Catholic Church's newfound success in France. It was created by Charles Flory, one of the founders of the Christian Catholic Church of France. The main intellectual of the movement is the world famous Soeur Marie, born Paule de Mulatier, a Carmélite sister inspired by the "Theology of small things" of Thérèse de Lisieux. Contrary to accusations, it doesn't try to reinstate the official link between the State and any form of clergy, and is a strong support to the Réformistes. The only reason why the two parties haven't merged yet is because of reluctance from some of the Réformistes.
The Parti Radical-Républicain is a center-left party, born of a short-lived coalition of the Républicains-Socialistes and the Parti Radical in 1933. It represents social-democracy in a more traditional sense, and doesn't question the existence of private property and conglomerates. There were mixed thoughts about the social policies of the Réformistes at first, but now that they have passed as laws it is out of question for RR themselves to question these new laws. They serve as "arbiters of the Parliament", debating laws depending on their own political agenda rather than on party-based considerations, but have thought of allying with the Alliance Démocratique for the elections of 1944.
The Alliance Démocratique is a coalition of liberal and moderate right, firmly laic. They are often nicknamed the "Lilies", due to the presence of many nobles in the party and the fact that François-Alphonse de Bourbon-Parme, nicknamed "Monsieur Plaisance", has become a figurehead of the Party. They are no longer fierce defenders of the republican form of government, but are nonetheless fiercely attached to the values of freedom, equality and fraternity. They are, in this sense, very similar to the Orléanistes of the XIXth century. They are the intellectual opponents the Réformistes have to deal with in the Parliament, not because of hateful rethorics, but because their critics are often very relevant and sensible.
If the Alliance Démocratique is the intellectual opposition, the Union Conservatrice is the political oppositon in the Parliament. It is a broad coalition that goes from moderate conservatives, who mostly wish to reestablish a more centralized state and a society based on the moralism and corporatism of the early Third Republic. They are also, ironically, much more republican than the Alliance, as they have been reinforced by anti-monarchist former Alliance members. They are still the leading right-wing movement, but have seen their results dwindle due to the overall success of the Réformistes and the greater credibility of the Alliance as a potential government party.