The imperial title was tied up to italian kingship : whoever controls Italy even partially, could have a chance.
Of course, being crowned does not guarantee at all it would last historically up to an HRE. For that, you'll need a relativly hegemonic power over nobility, having enough ressource to enforce the title.
Basically, anyone that can't have access to Italy are out, feudal fragmentation makes France having low chances, Italy as a whole isn't powerful enough.
The possibilities are clearly low.
A detail, the name of the empire.
"Holy" appears only during Otton III, in a epic move to piss off Byzzies (before that he had the same title than Basileus aka, Emperor of the Romans) and to keep pontifical power (that used the same title of "holy") institutionally challenged.
"of the ... nation" appears only in the late middle-ages, in order to keep the imperial title for themselves, insisting on a non-universal role to prevent neighbours to intervene, and to prevent inside non-german nobles to takeover.
It's really not a given that these terms would appear in an ATL.