What is the relationship between the Middle Frankish Kingdom and the Holy Roman Empire?

The Middle Frankish Kingdom, or Middle Francia, was part of the Carolingian Empire, the empire established by Charlemagne. It had nothing to do with the Holy Roman Empire, which was established seventy-four years after the fall of the Carolingian Empire.

Middle Francia was created with the division of this the Carolingian Empire into three parts. Each one was given to one of the three sons of Emperor Louis the Pious. Middle Francia was given to Lothair I the eldest son. It comprised Holland Belgium, eastern France from Belgium to the Mediterranean coast (Alsace, Lorraine, Burgundy/Bourgogne and Provence) and Italy. One of his brothers was given West Francia (the rest of France) and the other East Francia (Germany, Austria and Switzerland). Lothair partitioned Middle Francia among his three sons.