The only possible way to have the same person as either the king of France or England would do homage, if they actually also held an Imperial for which they need to do homage. However technically it wouldn't be the king of England or France, still there's a high chance of occasions of similar awkwardness as IOTL existed between the Norman dynasty (after the Norman Conquest of England), later the Plantagenets, and France.
As for the relationship between the Holy Roman Emperor and the king of France, they were the two most prominent Catholic princes; though a crowned Holy Roman Emperor would lead the order of precedence, even after the time, when the actual situation had changed, this (symbolic) courtesy remained.
That's something completely different than having the king of France doing homage to the Emperor; Bohemia was an exception not the rule (only replicateable, if another Imperial Fief was raised to a kingdom, which is unlikely, but not totally impossible). The Empire had various points, when they were strong, requested fealty from the rulers of Denmark, Poland and Hungary; but it rarely occurred and never lasted long enough to structural.
Maybe in a TL where Lothar manages to defeat Charles the Bold and Louis 'the German', there might be a situation, where kings end up doing homage or at least swear fealty to the Emperor. Though there wouldn't be a Holy Roman Empire as we know, and Francia Media probably needs parts of West and East Francia to be able to dominate them, so no France as we know it either.