This seems to be the consensus here - that a Umayyad victory at Tours/Poitiers could not be decisive and that the Franks would eventually drive them back - but I'm not completely certain of that. Many of their invasions from the 632-732 period were with smallish armies that won surprising victories. Tariq's invasion of Spain in 711 seems positively insane in retrospect, yet it succeeded and led to a 700-year presence in Iberia.
One thing that is pretty much certain is that the Umayyads would need reinforcements to hold down Gaul. This would require the Berbers not to revolt, so a TL dealing with a Tours victory has to find a way to avoid that. But I think it can be done.
Not necessarily all of Gaul, to profoundly change the course of Western history (and therefore, global history): If the Umayyads can not only hold Septimania and then onto say the bulk of Provence. They get just about full control of the Western Mediterranean, for some indefinite time; distinctly side-track if not cause the Carolingian Empire to be still-born; and pretty much limit the
Reconquestia to at best Atlantic Iberia (Portugal, Galicia, Asturias).
Ironically, having a culturally vibrant, and geopolitically potent Umayyad Caliphate on their doorstep for few more centuries could very well have a lot more positive effects on Western Europe than what really happened.