Excerpts from Books and Wikipedia
"Charlemagne was survived by only one son, Louis the Pious, who inherited the whole empire in 814. . . . In 817 he appointed his eldest son, Lothar, sole heir to the empire. . . . this settlement began to unravel in 823 when Louis the Pious's second wife, Judith, gave birth to a son, Charles the Bald. Judith naturally wanted Charles to inherit a sub-kingdom of his own. Louis's older sons anxious that this might diminish their inheritances, opposed her. Louis spent the remainder of his reign struggling to find a settlement acceptable to his wife and his increasingly rebellious sons. . . . As soon as his father was dead, Lothar attempted to seize the whole empire. Despite their animosity, Louis the German and Charles allied against Lothar and defeated him at the Battle of Fontenay in 841. In 843, the empire was divided into three kingdoms at the Treaty of Verdun: Louis receiving most of Germany, Charles most of West Francia ('France'), and Lothar everything in between. It was from the breakup of Charlemagne's empire, which began at Verdun, that over the next century the kingdom of France, Germany, and Italy would emerge." [1001 Days]