This has not to be made in the same way of the Chinese. I am not talking about Charlemagne's heirs campaigning in Spain against the Saracens: just support the local entities (first Kings of Asturias declared themselves vassals of Charlemagne, even if only in name) to do a quicker Reconquista and keep these resulting Hispanic entities under your umbrella, like IOTL Bohemia or Croatia at early 800s.
Then, we might need to have a PoD in the first campaign in Spain. Nothing that would remotely look like a reconquista I agree, but I could still see, a partial conquest of vassalisation of Ebre's basin by Carolingians.
We know that, in 765 and 768, Franks and Abassids exchanged ambassies at the initiative of Peppin III. Would he have lived a bit more, you could have seen earlier Carolingian expeditions in Pyrenean Iberian peninsula, comparable to what Charlemagne and his son eventually pulled out : it would be as much territories being possibly used as a stepstone for later campaigns.
A future equivalent to Paderborn's embassy could as well ensure more Abassid's support (remember that Abbassids were able to pull two, while unsuccessful, expeditions and revolts in al-Andalus including Abd al-Rahman ibn Habid al-Siqlabi's revolt that was likely made in cunjunction with Paderborn's embassy) or at least a more efficient one with the support of part of Ebre's Arab nobles.
It could then lead to a support and possible clientelisation of north-western andalusian polities with the conquest of key positions north of Ebre, at least until the revolt was crushed.
The main problem is that these same Arabo-Andalusian lords weren't exactly thrilled at the prospect being clientelised and possibly threatened by closer Franks, especially when they suffered recent and regular defeats against them.
Basically, you'd need a more successful pro-Abbasid revolt in al-Andalus, to make these nobles more solid when it come to the Abbasid-Carolingian alliance in Spain.
If it fails, or if Arab nobles eventually refuse Frankish presence as IOTL, you'd have at best a superficial conquest of transpyrenean highlands as IOTL, bonus or minus some places.
I couldn't say exactly which places would be taken by Franks in this expeditions, but I think it could give something like this as a maximal range (on left, with IOTL situation for early 814 on right). Not immediately, but over different expeditions, swalloing up of submitted Islamic principalities, etc. in 810's/820's.
Basically, an extension over most of Pyrenean highlands, with
- Gasconia ulterior (south of Pyrenees) being more importantly developed (which may make the big Basque revolt less successful IOTL)
- Marca Hispanica/Tolosana being slightly reduced, but expanding up to Ebre
- Asturias acknowledging a relatively formal Frankish overlordship, while expanding more quickly in the same direction than IOTL (roughly the situation in late IXth)
- al-Andalus, either pro-Abbasid or not being more likely fragmented outside core areas into principalties (keeping in mind that whoever is in charge would have a relatively easy time not only ensuring overlordship but increasing his power over time) possibly with earlier concession to muladi (or Christian princes as in Murcia)
Over time it could mean a lasting Kingdom of Aquitaine, would it be as a sub-kingdom, giving a more important hold in Spain of his nobility (especially Gascon and Tolosan);
I think it is more to keep a somehow united core (France/Germany/Alps/North Italy) with lot of peripherals,.
It's unlikely to keep most of southern European regions as a core :
think along the lines of the planned split of 806
Certainly if they had kept all of France and Germany as a united core.
With the rise of landed aristocracy, this is going to be hard to achieve. An unified Carolingian ensemble would be ambitious already, let alone united.
The best way to get around the problem of division without turning it into an eternal problem of civil war is to be continually expansionist
Thing is, outer territories are either too poor to be really attracting, or too powerful (Spain or Byzantium). Not mentioning that inner strifes aren't only caused by redistribution issues (but as well, maybe more, by growing independence of nobility). In several regards, Caronlingians mostly managed to secure the old Frankish sphere of influence, and control it more tightly than during most of Merovingian era : but it was fairly unstable and based on immediate and strong conquest, which couldn't be enforced eternally.
Giving the pressure from Scandinavians, Arabo-Berbers and Maygars at its fringes, the Carolingian ensemble would be lucky enough to keep its marges especially in Eastern and Southern Europe.