Well, to determine the worst claim, we should probably determine who has the best claim. The only polities with valid claims are those which existed contemporaneously with the Empire. Thus, Spain, Greece and modern Italy are disqualified. If there was a through line between medieval and modern Italy, then matters would be different, but in discernible respects outside of certain cultural affinities, Italy does not fit the bill. Greece is in some ways in a similar position to Italy. The French claim is more interesting, but really only works if one wants to argue that Charlemagne became the proper Roman emperor in 800, which given that he was only declared Holy Roman Emperor in part because a better contemporary claimant existed, he too is disqualified and whatever iteration of France is along with him. Disqualifying Charlemagne arguably disqualifies the later Holy Roman emperors too, but not necessarily or entirely for reasons I'll hit on later.