As long as Napoleon admired Charlemagne (he visited his tomb in Aachen) it is not strange that he would come up with this idea.
I know he was strongly advised to do not take the HRE title but he could have forged a completely new title like Emperor of the French and the Germans. In fact, the reality would not be that far from being a Protector of the Rhine Confederation, but he could have the power to remove annoying German aristocracy and simplify the administration (no need of sister republics in Batavia, Switzerland etc.) with just a French Imperial realm west of the Rhine and a German mirror east of the Rhine.
I know he was strongly advised to do not take the HRE title but he could have forged a completely new title like Emperor of the French and the Germans. In fact, the reality would not be that far from being a Protector of the Rhine Confederation, but he could have the power to remove annoying German aristocracy and simplify the administration (no need of sister republics in Batavia, Switzerland etc.) with just a French Imperial realm west of the Rhine and a German mirror east of the Rhine.