It's a tough question, because solidifying control over the peninsula in the wake of Umayyad conquests can mean a lot of both contradicting and not-contradicting events talking place.
For instance, it can easily mean, or even requires, a successful set of campaign by Al-Sahm in the early 720's culminating with a victory over Aquitanians : probably not a full-fledged conquest of the region, but very probably an at least temporary occupation and garrisoning of an area between Toulouse and Avignon for the next decades.
That would have also the potential outcome of preventing whatever happened in the Cantabrian highlands in the same rough time, but that could easily be treated as an incidental additional event.
Giving the context (that is of limited number of settling Arabo-Berbers), I don't think we'd have a massive socio-political change compared to IOTL in these marginal regions : that is establishment of garrisons in key cities, requisition of up to one-third or one-half of the land, etc.
Most of these immediate changes would happen in this region (let's say between Toulouse and Avignon), Asturias being a bit too remote and poor and probably not changing that much from IOTL 720's at the exception of its rebelliousness, would it be only due to being more "militarized" and as a hot march, when it comes to its role in raiding and campaigning (a profitable and politically necessary endeavour) against Franko-Aquitains.
IOTL Asturias wouldn't be untouched, in fact it'd be very possible in this configuration to see local aristocracy electing to convert to Islam, as a large part did in the rest of the peninsula. In the North-Western region, you'd then see instead of a largely autonomous Christian aristocracy being slowly integrated within a sole entity, a series of either Christian or Muladi dynastic holdings whose nobles would have a more invested interest competing for access to the waliat and then emiral connection.
On the other hand, while I don't think that change in itself much about the Peppinid dominance in France, pretty much rooted in all structures of power since the rule of Peppin the Young and Charles own victories. That being said, a much greater Arabo-Berber presence in Gaul would certainly have consequences there, as you'd likely see earlier attempt at raids in the Loire basin akin to the raids of 726 or 732. I doubt it would translate as an immediate focus on them, however giving Charles even in the wake of the 726 raid still focused on fighting Bavarians, but much weaker Aquitanians and the more pressing threat over upper Burgondia or even Austrasia would cause likely more alarm ITTL.
I don't see any good reason why things would unfold militarily much differently than IOTL there, except that the Aquitanian defeat in 721 might simply butterfly away the raid of 732 as it happened and actually focus more along the Rhone river, but overall I'd say it would be a slower, maybe more diffuse and harsh conquest of cities and strongholds by Franks, building up some idea of prime confrontation with Arabo-Berbers, a more "Mediterranean" tropism if you will than IOTL.
So by the time an equivalent to the Berber Revolt happens (somewhat inevitably at this point, IMO) along with the consequence of the Fall of the Umayyads (likewise) we basically have to deal with a set of either Christian or Muladi petty principalities in the North-Western corner, and a more "aware" Charles dealing with raids/counter-raids and maybe more intent on taking back lands as he was IOTL (maybe not turning away from a siege as he did in 737 after his victory).
With a troubled time of Islamic Spain, and this approach, I could see Charles' immediate successors pulling equivalent large campaigns as Charlemagne did IOTL in Spain (especially if they don't go for other peripheral regions) with the support of competing Arabic, Berber, Muladi and Christian aristocracy (always potential, but very unreliable, allies) and the constitution of a larger (both northern and southern wise) Marca Hispanica. It's not really a natural outcome of the PoD but something that can be streamed towards.
A more "mediterranean" Carolingian Francia, however, might be also more fragile : Carolingian (re)conquests in Germania more or less supplied the approbation of a relatively tiny imperial aristocracy with lands and loots, along with other revenues partly born out of trade with North Sea *and* Muslim Spain (including slave trade), so while it might creates a foundation for a more important Frankish presence in Spain early on, I doubt it would even in this case translate as an early takeover : possibly more an early power fragmentation into aristocratic-led "regna" (very long story short, these were kinda the equivalent of stem duchies, but more heterogenous and not at all unified, in western Francia) comparable to what existed in the early to mid-Xth century before the feudal fragmentation. From there you could work your main idea.
