Could you expand on this?
Well, for starters, the "political horizon" of Franks tended to entierly include the regnum, complete with peripherical duchies
The first motivation of Peppinids/Arnulfids, once they managed to unify the three proper Frankish sub-kingdoms (Neustria, Austrasia, Burguny) in the late VIIth was to impose their authority over the peripherical duchies of the regnum(Aquitaine, Bavaria, Thruningia, etc.)., or even the peripherical entities out of the regnum (Frisians, Saxons, Gothia)
Where modern French geostrategical horizon tended to a sanctuarisation of the territory (altough one could stress that Capetian ambitions were to slowly eat on their immediate neighbours) Peppinids/Arnulfids were more focused on recovering the entiere regnum at their benefit : for instance while the Arabo-Berber raid of 725-726 plundered the entiere Rhone valley, and either stopped at Autun, but possibly at Sens (which is less than 100km from Paris, N-E, for localisation purposes); Charles prioritarized his campaigns on Bavaria.
I'll make a leap backwards on time there : While I can think of two Frankish participation in Spanish matters (in 632 with Dagobert's support of Sisenand, in 672 the support of Paul' rebellion), there was not I can think of in Italy for the same time, while Dagobert more or less campaigned everywhere (forcing Saxons to be Frankish tributaries, pushing back Vascons, meddling with Brittany, and campaigning in Central Europe with Lombard support against Slavs). We have to constate that there was no Italian strategy for Franks at this point, and relatively late so.
Eventually, while Peppinids/Arnulfids/Carolingian did first focused on establishing their control of the old regnum, most of campaigns after that give a large part to political and economical matters : the takeover of Italy was less dictated (we saw it) by a Napoleonic-like geostrategical vision, that how undergoing it was decisive for inner politics. And even before Charlemagne, you didn't had much tought to an outright conquest, than sattelization of Lombardy (Pepin III's matrimonial policy with Lombards, for exemple) : but the support Lombards gave to peripherical duchies as Aquitaine and Bavaria, and critically the support they gave to Carloman's son claims, plus the pontifical-Carolingian alliance (which was determining into strengthening the latter legitimacy) helped a more...decisive resolution.
You'd notice that in the Ordinato Imperii of 806, Italy was treated as a separated kingdom to be, as Aquitaine, while Francia proper would take the lion's share in North Sea and Central Europe.
Similarily, you did initially not had a huge drive on Spain, as it happened for Italy. Carolingian's objectives on this matter were less than clear, except benefiting from a call to help from andalusian revoltees (initially formenting a pro-Abassid rebellion for some). It pathetically ended, mostly because al-Andalus for all its structural weakness was a strong polity (which Carolingia, must it be said, wasn't).
In the case of a Visigothic survival, however, while you'd certainly have such call to support (as Franks recieved during the VIIth), the structural weakness of Gothia would play more favourably for what matter Frankish intervention : not that I think they would that bother with replacing local nobility (they almost never did, with the big exception of Frisia, Bavaria and Saxony, on which they get rid of part of the local elites due to particular resilience), but the capacity of resistence of Goths before a Frankish intervention would be small.
Probably that several Gothic potentes would escape a real Frankish presence, as southern Lombards duchies did : in spite of being tributary and technically vassals to Franks, they were their own thing for all the period.