The army desperately needs more men, which means recruiting among the native population, which means providing incentives in terms of civil rights. It's a short-term calculation but with long-term consequences. Besides, OTL has amply demonstrated that De Gaulle had no qualms about throwing the Pieds-Noirs under the bus when they didn't get on with the program.
Metropolitan France is under German occupation, with an illegitimate puppet government of opportunists and extremists who (even more so than OTL) are constantly at loggerheads with each other. Nobody there gives a damn about what's going on in the colonies; there are more urgent matters do deal with such as finding enough food to survive.
Perhaps I'm just not explaining it very well.
North African units already played a substantial part in the WWII IOTL without substantial promises of reform. Afterall, Algiers was the capital of Free France from 1943, and the authority ignored the demands from the Muslim Algerians in form of "Algerian People's Manifesto". Calls for moderate reform, including the abolishment of Code de l'Indigénat did not materialize, and Crémieux Decree was barely reinstated. The calls for independence immediately after the war was met with massacres in Setif and Guelma. You have to admit, it all does sound rather wish-fulfillment-y compared to the OTL.
Furthermore, we are talking about De Gaulle in 1941, not 1958. He argued that the "Mission Civilisatrice" precluded any thought of autonomy or any possibility of development outside the French empire, and that "Self-government must be rejected - even in the more distant future". at the end of the Brazzaville Conference in 1944. De Gaulle's response to Paul Mus, on his counsel against intervention in Indochina is telling: "Dear Professor, we will win because we are the strongest".
I'm talking about this because I find the concept fascinating and worth going deeper into it, but it does seem like the timeline is heavy on the wish fulfillment and less on deep consideration what the Third Republic was. In that vein, I'd argue that the most plausible POD for the "France Fight on" would probably be successful SFIO-led Popular Front with a massive political capital that confronts the Third Reich during the Sudeten Crisis with Soviet support.