We know that the effect on Europe was so complex and confusing that, in general, we don't know what happened. The differential impact of disease would of course logically affect different core and periphery regions variously. Moreover, the Byzantine state was aggressively conquering still more indefensible territory at the very time the Plague struck, but increasingly overtly waged war for the purpose of predatory taxation of former subjects of Arian Vandals, Ostrogoths, and Visigoths it had originally made Holy War to, as we would say, Liberate. Colder climates being more salubrious, when even feebly exploited by improved agricultural techniques, the soils of Northwest Europe were so superior to the old Mediterranean ones that they provided the basis for a new core area.
Sheer guesswork goes a long way, the seventh century reaching a new low in surviving documentation.
Even later, the exulting of a Beckwith over the glories of the Carolingians at their height ignores the superficiality of the edifice. At the Carolingian peak, nobody would have imagined any such entities as France or Germany. Both were Germans and Frankish. In 589, Wen Di of the Sui dynasty, who had, as General Yang Jian, a half- Mongol nobleman, seized power from the Northern Zhou in 581, the latter having only in 577 destroyed the Northern Qi and unified North China with Sichuan, defeated and captured the hapless Chen Shubao, last ruler of the Southern dynasties ruling in Jiankang since 317. There is every reason to beliieve that Chinese exports were inelastic.