I wonder, if we assume that the Empire keeps at least a large enough area to deserve to be called an empire, what effect would this have on the development of the papacy? In OTL, for a couple of centuries there were no western empire (until the rise of the Carolingian empire and the later HRE), but what if there were a western empire lasting at least till approx. 1300 AD?
The butterflies in general would of course be huge. The POD is several centuries before the rise of Islam, so Islam would be butterflied. North Africa would keep having strong ties to Europe, so the concept of Europe as a cultural area would be far less important. Southern Europe would probably keep having stronger ties with North Africa than Northern Europe.
I am not sure how the collapse of the empire could be avoided, though. Somehow the invading Germanic tribes would need to be assimilated orn kept out. How do we avoid that different groups conquer different parts of the empire?