You'd probably have to go back to the 1930s and get more fast-track popularity of an allied Québec-based party much sooner than OTL, making discontent with Taschereau's provincial government happen much sooner. While we had to wait for Saskatchewan to have the break-through for social democracy IOTL, why not make the move sooner? The discontent was already there, and it would provide a healthy (nationalist) alternative to the Union nationale/Duplessis and nationalists like Abbé Groulx. In effect, it would be an earlier Quiet Revolution/Révolution tranquille with the proto-version of what IOTL would become the Bloc populaire.
The CCF was not trusted because it was an English-Canadian party inattentive to Québec's specific needs (as opposed to the needs of French-Canadians as a whole, which Québec abandoned as being a national identity of weakness) and socialism was seen as bad among the clergy. But, there was already an active and growing labor movement, particularly in tandem with the growth of Montréal as a major city. There were already areas in Anglophone Montréal which had ridings provincially (and IIRC federally as well) which were supportive of labour and worker's parties, but that won't be enough. Instead, the CCF is going to have a relationship with Québec much like post-war Germany IOTL, where the CDU has a special relationship with Bavaria. If the CCF can tolerate an independent Québec-regionalist (it was not yet nationalist during the 1930s IOTL) social-democratic party which would be neutral on the subject of World War II, because many Québécois/es were indoctrinated with anti-conscription rhetoric malgré eux, due to the disaster that was World War I, so as a result many in Québec were anti-War - baffling those in France who befriended French-Canadian intellectuals (André Laurendeau's French friends, for example, remarked to him, "We don't understand your position. You should be fighting the Nazis.") - then maybe, just maybe, the CCF could get its breakthrough by taking advantage of the tendency in Québec to vote as a bloc with what they thought would be the winner most sensitive to Québec's issues.
A Parti social-démocratique du Québec provincially, with its federal wing as the Parti social-démocratique du Canada, who would be able to get along with the CCF and translate it successfully to Québec's specific needs (even more so if it was in Government provincially) could help out a potential CCF Federal government considerably, no matter what the clergy thought with their whole "heaven is blue and hell is red" shtick. As much as one can tweak with the results in English Canada (which, by necessity, includes the French-Canadian communities outside of Québec), it would certainly make life easier for the CCF if they had a tangible example to show to the rest of Canada that socialism can work, and especially a socialism not reliant on the Soviet model as the Communists/Labour-Progressive Party advocated, and Québec could provide the model. The Swedes had the concept of the Folkhemmet; the Québécois/es could (as they did in the Quiet Revolution) reappropriate the old French-Canadian slogan Maîtres chez nous (Masters of our own house) for its own ends, and if socialism could work as a renewal of Canadian federalism as a whole, such as it was in those days, then by all means. (The only difficulty I would see for that is the Regina Manifesto specifically calls for the abolition of the Senate, which leaves questions in my mind as to how the provinces and territories would be represented in Parliament, such as would be the case in the 1930s and 1940s and long before the modern conception of the First Ministers' Conference came into being). It would be interesting to see how CCF/PSD Governments would operate as such ITTL.