This is going to end wonderfully (sarcasm). So ITL Nasser gets his dream as there is no Israel to be humiliated by? Just to clarify this means the Free French are domed?
He and the Pan-Arabist ideological community have already achieved significantly more progress in their goals then they ever did in OTL (partly because Israel never existed yes, but because of many other factors) And thus Egypt has been able to successfully incorporate Palestine and Jordan without much trouble so far. I of course cannot divulge too much in future plans for the UAR due to spoilers; but I can say that Nasser and the UAR are going to be getting
really busy fairly soon.
It wouldn't surprise me if the French are forced to abandoned north Africa in not to long. Even if Nasser and the UAR never get their hands on it the Algerian rebels could be enough to eventually drive the French to South America (Guiana) unless France is willing to do some horrible things to stay. More likely though, I think this will become Vietnam in the desert with ACT/French forces being bleed to the point they decide holding Algeria isn't worth it anymore, or just can't do it anymore.
Actually before the war in Algeria most Frenchmen considered it part of France. Secondly when it did French settlers started terrorism against Algeria and France. Plus retreating to South America means communication with anti Vichy guerrillas in the homeland difficult.
While all of this is very very
true What if, however; I think there is one factor that you must account for in this instance regarding the French. That factor is of course the fact that the Algerian War of our own timeline was fought by the French government from the comfort of Paris, ITTL, we instead have the remnants of a the democratic French government fighting for it's very survival in the last bit of "integral France they have". If how hard France fought to try and keep Algeria from gaining independence in our own timeline is any inclination, that factor would only be even more severe ITTL. As for the Free French Movement, not only is Algiers their capital; but it is their last little shred of legitimacy that distinguishes them from the Vichy government on the mainland as well. Losing Algeria would literally be the most catastrophic that could happen for the French here because it would essentially result in the complete destabilization of a Democratic French government and the Free French movement as it is known.
What is a certainty it seems is that this whole ordeal in Algeria is going to be very
very messy, especially now that the Nazis and Nasser are sticking their noses into it to try and destabilize De Gaulle and crew.