The sons of Louis the Pious never had the fortune to be sole children. Among their Grandfather Charlemagne's children, Louis was the only one to reach adulthood. So the Carolingian Empire endured for another generation. At the end of his life, he divided his realm among his three sons, Lothair I, Louis the German and Charles the Bald. They received the Kingdoms of Middle, Eastern and Western Francia respectively. With Lothar I succeeding his father as Emperor of all Romans and Franks. This arrangement was named the Treaty of Verdun.
Lothair I died an early death, with three sons of his own he divided Middle Francia into 3 lesser Kingdoms. But his brothers in the East and West claimed suzerainty over his lands and invaded and divided his dwindled realm among each other. West and East Francia would eventually become the Kingdom of France and the Holy Roman Empire.
That's not entirely correct the way it's phrased:
East Francia developed into the kingdom of Germany (later absorbing the duchy of Lotharingia) while Italy (Lombardy) and Burgundy remained kingdoms in their own rights (multiple ones in the case of the Burgundies) only to eventually form up a union with the German kingdom which would end up to be called the Holy Roman Empire in the 13th century.
Beautiful work as usual. Spotted one mistake though: Rijnsburg is located farther north, near the mouth of the Old Rhine (Dutch: Oude Rijn). Here it's drawn at the mouth of the modern-day main branch of the Rhine, near Rotterdam.