I think determinism will always play a big role in any opinion given here. Trick is managing it, without discounting the possibility of how different things actually can be.
Roman empire was a Mediterranean based empire right from the get go. Any version of a stable, prosperous and politically united empire, recognizable as the same entity from centuries ago, SPQR would still be Mediterranean based. Like any Chinese Empire, which was culturally Han Chinese, would have the Yangtze as the center of it's economy/population/culture. Same for North Indian empires and the Gangetic plains.
In our timeline for example, it was the Carolingian age from about 500 CE to 800 CE which saw intensive deforestation of Germania and increase in northern European population density due to the northward shift of political power. I reckon this would have created a cyclical effect where as feudal power centers multiply and grow, so does their demand, turning the former gallic provinces into a much larger producer of grain, further increasing population sustenance capacity.
I would argue that the early medieval (relative) political isolation and the late roman breakdown of the urban Mediterranean economy, was a major factor why Northern France emerged as such a demographic powerhouse. If the Imperium survives in a recognizable form, I'd say chances are that Constantinople and the Bosporus retains it's economic hegemony, politically domination by Rome-based Nobility, and Egypt is maintained as the perennial cash cow.