I don't see it falling apart from within, honestly. It wasn't doing so.
There was a big difference between the Caliphate and the Visigothic Kingdom, a difference of "state psychology" or something like that. The Caliph was a religious ruler. The country was dividided in independent-minded emirates that got along because all of them followed the religious dictact of the Caliph. Once that Caliph dissappeared, the emirs pursued their own agenda, as there was nothing to link them aside of religion - and this wasn't eaxct either, as once the Cordovan Caliph was gone they could and did choose different Caliphs in North Africa to follow... spiritually and from the distance, of course. The lack of internal cohesion could be tracked to the same Muslim post-conquest policy of dividing the land between emirs of different ethnic backgrounds (Berbers, Syrians, Yemenis...). Said policy decisively contributed to erase the links between the Muslim provinces and any idea of being part of something between the province and the Umma.
The Visigoths, on the other hand, had the Kingdom. Whatever happened, there would be a kingdom. A local nobleman could rebel, but never with the idea of secceding his piece of land, but with the idea of using his base to take over the throne and the whole kingdom. Isidore of Seville's writings prove that there was some kind of proto-nationalism at the time in the sense that the kingdom existed and would exist, and that the kingdom was based on, and in some sense was, the (Hi)Spania. In this sense they were like the Roman usurpers: They rebelled in Britain of Gaul, but never proclaimed themselves King or Emperor of Britain or Gaul... they wanted to be Emperors of Rome, and Emperor of Rome was the only title worthy of earning. When the Witizans invited the Muslims in, they though they would be mere mercenaries and depart as soon as Rodrigo/Roderic was killed. It was a surprise they didn't. In fact, before going to the Muslims, the Witizans considered but didn't bribe the Byzantines because they remembered that somebody did that a century before and the Romans decided to sit in the southern part of the Peninsula. They talked with the Franks, too, but canceled any talks when they asked for the province of Septimania in return. Who knows, maybe they trusted the Berbers because the Witizans didn't realize or understand that the Berbers were now ruled by the Caliphate and weren't a bunch of independent gold-hungry tribes anymore. In any case, it proved to be a very big mistake.
A Frankish takeover? Impossible I would say. First, because Charlemagne went actually to war against Pagan rulers and nations only, using Christianity as a tool in his favour. That wouldn't work against the Visigoths, who were Catholic. Second, because the Franks lacked any sympathy in Hispania, and were seen as The Enemy with capital letters since Vouillé. The fact that Charlemagne was unable in OTL to establish a frontier on the Ebro despite the divisions between the Muslims (he was invited in by the commanders of Barcelona and Zaragoza) and the lack of identification between the rulers and the people (80% was Christian in "Al-Andalus" at that time, at least) says very little about the Frankish options. If any, the Franks could hope to back a Visigoth rebel and hope to establish an alliance, or to get a peripheric province like the Septimania. But if they tried to conventionally invade the Peninsula, the more they could achieve was to unite the Visigoths against them and fight in a logistic nightmare. In fact, if the Visigoths were on the offensive, they even could play the romanized peoples around Massilia against the Franks (as the Muslims briefly attempted in OTL) because they still remembered the Ostrogothic rule with sympathy.
If any, I can imagine, though, a possible decreasing of centralization and growing feudalization that could reduce the royal role to something ceremonial, as it happened after 900 in France and Germany. But the office of king would still exist, and they probably would still punching each other on the face to achieve it. Unless, who knows, a king named Roderic is able to exploit some big victory in 711 and successfully introduce the hereditary monarchy...
. Remember he was Charles Martel's grandson, and Martel might not have seized power without his victory at Tours.