I'm on the fence about the future political evolution of France. On the one hand, there will be no post-Vichy cleanup, nor will there be the resistance-forged consensus which critically held up in 1944 to allow some sweeping reforms. On the other hand, there won't be a strong PCF, which was a major pain in the back for the IVth republic, and the attraction of TTL "gaullism" - the idea of a sweeping reform of the State along, hm, "executive-favouring" lines - will be made weaker by the absence of a de Gaulle, precisely. And many of the drivers that OTL led to the reform of the State will be present: the reinforcement of the executive was well underway by 1939; and the war will have given a shot in the arm to the partisans of State intervention in the economy, like OTL.
I don't know if a post about that era's french politics is a good idea, feel free to skip if it's getting too long - but in a nutshell the problem is that OTL the war caused a temporary but drastic clarification of french politics, and that there is no easy answer to what other paths this clarification could have taken. Of the three major forces that dominated french politics in 1940 - the socialists, the "radicals" (centrists) and the new right around La Rocque - only the first had survived in 45, and having undergone a good deal of ideological transformation - and two new ones had risen: the Communists and the Christian-democrats. So, what of them ITTL?
1. The socialists
Before the war, the SFIO was marked by a degree of undecisiveness caused by the tension between the party's traditional/radical wing, which preached revolution and mistrust of the state, and its mainstream, which had embraced social-democracy in all but name. This was exemplified by Blum's rhetorics in 1936, explaining that the left had not "taken power" but was merely "exercising power", which meant that he unfortunately couldn't put into practice the proposals of the far-left. That said, the SFIO experienced the first really executive-led government in France in 1936, and some among them had really clear ideas about the future of the economy. OTL, the war led to a shift towards embracing humanist social-democracy among much of the leadership - exemplified by Blum's publication of À l'échelle humaine in 45, written in german prisons, where he conjured his fellow socialists to engage in democratic reform. But the pressure of the PCF on its left wing led to a backlash: post-46, the SFIO began coating its reformism in revolutionary rhetorics again.
TTL, my opinion is that the same evolution as OTL will more or less take place. During WW1, the experience of state interventionism in a war economy kickstarted many soc-dem ideas about interventionism; if I'm not mistaken, in WW2 it also gave credibility to Labour's plan. TTL, the SFIO will have been co-steering a de facto mixed economy for two years, will have had increased contacts with their Labour peers, won't have the PCF on their shoulder, so I strongly believe they will endorse the mantle of reformism with a clear-enough program. One point for stability.
2. The radicaux
Radicaux used to be radicals, but that was in the XIXth century. By 1940 they're basically a party of the small bourgeoisie which claims to defend left-wing value: their spirit is embodied by the idea of defending "les petits contre les gros", ie small (shopowners, landowners, businessowner) against big (industrialists, etc.). They kept a strong appeal both because of their comittment to the Republic and because there was no other party really defending the interests of the middle class, with the SFIO focussed on workers. Problems started to arise when their economic conservatism and their narrow understanding of the republic got in the way of genuine reform: they wanted neither strong state intervention, nor a strong executive... However, OTL they went a long way towards modernisation between 36 and 40, with the "young-turcs" of the party (that's really how they were called) gaining audience (cf. Reynaud) and Daladier embrassing Blum's ideas of executive-led parliamentarism. They were savagely crushed in the first elections after the Liberation because they had so strongly associated themselves with the IIIrd Republic, and had been in power in 1940.
TTL... I think a lot hinges on their capacity to renew themselves and clarify their position. After the war, they will certainly agree to a degree of reform - be it only because, well, the brunt of it has already taken place between 1936 and 1942, with stronger state intervention in the economy and a stronger executive. But they will certainly be crushed to some extent between the SFIO and the right, unless they manage to embrace a more liberal modernism than the SFIO - which demands they shed some of their conservatism, which I'm not sanguine about their odds of. OTL, their most brilliant postwar politician was Pierre Mendès France, who... well, didn't really prove up to the task.
3. The right
This one's a bit of a wild card.There has been much historical debate to know whether the cristallisation of the french right in 36 - 40 around La Rocque's PSF - which was the first really big french right-wing party - was the symptom of fascist infestation, or a forebearer of the christian-democrat party that would feature prominently in postwar french political life. The PSF was tainted by its ambiguous attitude under Vichy (ambiguous as in: we expected to be in government but aren't), and disappeared afterward. Without giving a definite answer, I'll simply remark that while the Vichy period was a catalyst for the right's swing towards moderation and the abandonment of antisemitism, there can be a similar if weaker evolution ITTL: pre-war, La Rocque had already moved a lot to distanciate himself from fascism and antisemitism, and one can expect the TTL events will have produced a similar effect.
The first question mark is whether they will have embraced the same ideals of social justice that the christ-dems embodied after 1945. I think there will be something of that: christian democracy in France didn't spring up from thin air. That said, they will be significantly more conservative than OTL christ-dems. The second question mark is about their commitment to republican institutions. OTL, there was a split within the right between the christ-dems, who supported the IVth republic, and the gaullists, who rejected it. TTL, I think this can only be avoided if there is a convincing degree of reform of the republic, since OTL the Right had been making calls for it since 1929 at least.
My personal opinion is that since a lot of the ideas and trends which drove the 1944 refundation of the republic were in place in 1940 and since the jolt of victory will be there as well to provide impetus, we would still end up with a reform at the end of the war: the PSF will be in favour of it, the SFIO probably if they can tie it to social reforms, and a part of the radicaux as well. I think we will have a reform of the republic that formalises the empowerment of the Président du Conseil, the prime minister, and gives a stronger role to the President of the Republic as well - something a bit like Auriol's activism OTL, but mayber stronger if the right get a say; tied in with a welfare package closely similar to OTL's one, and to all the same packages seen in western europe at the same time.
As well, french politics will be both more consensual and more conservative than OTL I believe. If reduced to the Hexagon, this "IIIrd republic and a half" could probably stand for a while...
... but the decolonisation will be a pain, probably even more than OTL.