The Great Translation

At its broadest, "the Renaissance" IRL means the economic and political upheaval caused by the Black Death and the end of the Medieval Warm Period, the changing power dynamics between Rome and the kingdoms caused by the Avignon Schism, linguistic changes caused by the rise of vernaculars and the rediscovery of classics (beginning with the Greek texts brought home from the Latin Empire, and accelerated as Byzantine civilization declined in its aftermath.)

And that's a problem for me. Because there's no guarantee that the Fourth Crusade (and there will be a Fourth Crusade) will result in the Latin Empire; there's no guarantee that church-state power dynamics will change because there may not be an Avignon Papacy; the Black Death could very well evolve in a different way. (Vernaculars and the end of the Medieval Warm Period, well, there's only so much that can be done about those.) Between that and a generally different intellectual landscape, there's no reason to think that the 13th century is going to play the same way, or indeed that it's going to be called "the Renaissance."

There is, however, going to be the Great Translation

Rinascimento is "rebirth." A return to an old form after some death: the death of Gothic art, the death of feudalism, the death of whatever the historian doesn't like. "Translation" (cf. translatio) could be two different things: "translation" (across languages) or "transfer" (across non-linguistic boundaries.) In the context of "the Great Translation," it means both. What the Western world experiences in those turbulent years is not a rebirth: it's an inheritance and a coming of age.

Basic notes on the Great Translation

Part of the reason Andalusada's historians talk about "the Great Translation" is that it's linguistically neutral; a more Catholic world will have more Latin formations, which can be held in common against, say, the hegemony of the Most Christian Kingdom.

As a general rule, the Great Translation involves two distinct and different features: 

Significant textual exchanges across languages: The process for this started in the high medieval, and (as usual) in Spain: IRL, Castile (based out of Toledo, IIRC) started serious translations of Islamic writing in the 13th century. At roughly the same time, Venice experiences a Greek revival from the sacking of Constantinople. From this came Averroism and such.

• Given that Toledo stays more or less under Moorish control, a similar effort would probably be seated in Aragonese Valencia or Zaragoza.
• No matter what happens to Constantinople, Hungary also gets a boost at about the same time, as a place for minority-opinion Greeks to go. It develops a notable "Orthodox scholasticism" that lays the groundwork for the future Church of Hungary, for instance, based on this period.

The second is the decline of the eastern counter-states. As of 1200, the eastern empires are very much powers in their own right. Over the course of the Great Translation, they decline considerably in prestige and importance:

• The fall of the Abbasid Caliphate: Even after it's abandoned any pretence of Umayyad legitimacy, al-Andalus considers itself the heir to the Umayyad Caliphate. When the Abbasids fall, the Moorish world officially declares that it won.
• The de-Arabization of the Levant: This period also sees the Muslim world becoming progressively less Arabic, as waves of invaders convert and colonize its heartland. Good old-fashioned racism really seals the deal here; al-Andalus isn't just the last holdout of the old Islamic world, it's the last holdout of the old Arabic world too. From this point onward, its historians alienate themselves from ash-Sharq, emphasizing the foreignness of its cultural developments.
• The decline of Constantinople: The Greeks fall. That much is foreordained - although by the time they fall, the border issues between Thrace and Pannonia have stabilized enough to allow Hungary a lot of access to Constantinopolitan texts.

What matters here is that the decline is longer. The longer the eastern decline takes, the more time Western Europe has to visibly appreciate that it's catching up to the great powers of its age. And it's the simultaneity of these two trends, happening at the same time, that allows for them to combine into a sense of transferred legitimacy.

Thus, for instance, Hungary's Anatolian Ostpolitik. Thus the fact that, after the Miramoline is driven into exile, her era is supplanted by Umayyad Seville.

Regimes come, regimes go, but the Rebirth isn't a new birth; it's an eternal recurrence.