Seems like this situation would be kinda tough if the Levant still falls to the Arabs, severing the ERE's land connection to Egypt. Also, Egypt was full of Miaphysite/Monophysite Copts who had quite a bit of bad blood built up with the orthodox Romans (hence why they found the first centuries of Muslim rule more tolerable than, and even preferable to, Byzantine rule), although by this time Heraclius was pushing
Monothelitism as a theological compromise to reconcile the Egyptians with and it had gotten further than previous attempts at compromise.
Anyway, if Byzantine Egypt holds, then besides the obvious (a much more Christian Africa) Muslim piracy remains contained to the eastern Mediterranean by Byzantine fleets operating out of Egypt & Anatolia, meaning they never wreck the Mediterranean trade network. That means Vulgar Latin won't splinter & evolve into the myriad Romance languages for probably a couple more centuries (historically that started happening in the 700s-800s due to the collapse of said trade network and the Muslim conquests of North Africa & Iberia). African Romance survives in the Maghreb and may evolve into its Romance own language centuries down the line: its speakers will have much more in common with Sardinians & Spaniards than they ever do Arabs, and I wouldn't be surprised if Northwest Africa is eventually identified as an extension of Southern Europe.
The notoriously chronically unstable Visigoth kingdom probably gets overrun by the Franks in the early to mid-8th century as well, not the Arabs who never come anywhere near Iberia. In turn, you might see a Frankish-led attempt at reviving the WRE still happen with Papal support and a (possibly earlier) Great Schism between the dyothelite West and monothelite East, as the Latin West was historically a redoubt of dyothelite sentiment and the theological dispute (which some Popes got arrested & tortured to death over IIRC) will provide a huge additional motivator for the Papacy to seek to get out from under the Eastern Emperor's thumb by any means necessary.