AHC and WI: French rulers get the title 'Holy Roman Emperor'

Your challenge, should you choose to accept it, is to have the French kings get the title Holy Roman Emperor and, most importantly, keep it. I guess one could start with Charles the Bald who was the king of West Francia (which roughly corresponds with France), but after that this branch of the Carolingians and successor dynasties should keep the title of Holy Roman Emperor instead of it reverting to the German kings.

Give it a go. Feel free to discuss the ensuing alternative development of Germany and France (I imagine the French rulers campaigning a lot in Italy rather than the Germans).
 
Charlemagne is less successful and does not conquer the future Holy Roman Empire. He is still crowned Emperor of the Romans by the Pope. This way, the rulers of an united France are the Western Roman Emperors.
 
I wonder if a longer living Louis II the Stammerer couldn't claim the Holy Roman Crown after his father...

Yet, you would still have to change the French Carolingians' bad luck after 879 and prevent the rise of the Robertians (Eudes, Robert I, Hugh the Great and his brother-in-law Rudolph of Burgundy) which lead to Hugh Capet becoming the first Capetian King of France in 987.
Although, if I do remember correctly, Capetians had a bit of Carolingian Blood in their veins. Wasn't it from Hugh Capet's wife?
 
Louis XIV had the ego to try it and enough influence to have a chance.

But I guess it would led to the collapse of the last working HRR institutions.
So what remains would be another empty title added to the French Royal Style and a stronger french involvement in Germany.
 
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