The contemporary Frodoard Chronicle describes the death of Charles the Bald as such: "Dans l'annee 877, le sixieme jour d'octobre, le tres exellent empereur Charles, de sainte et illusmemoire, termina sa course terrestre, et a ce que nous esperons, entra en possession des joies eternalles. Il fut reellement fils du serenissime empereur et auguste Louis, et petit fil du tres glorieux Cesar, nomme Charles." Guizot 69

Carolingian succession was rarely clean, and continued its pattern of internal conflict and political uncertainty after the death of Charles the Bald in 877. Since the key to this is a series of family relationships, you might want to look at an abbreviated genealogy of Charles the Bald and his brothers and descendents. The same names keep repeating themselves, making it confusing to keep track of the players. CB had three sons; Louis the Stammerer, Charles and Carloman. During his life, the sons revolted and the father crushed the rebellion. Louis ended up in Aquitaine, Charles died in 877 and Carloman, who was blinded by his father, died in 876. At the same time, Charles found himself in conflict with his brother, Louis the German and his nephew, Louis III, over territory in Italy and on the northern borders of their joint kingdoms.

Louis the Stammerer inherited from his father Charles the Bald, but, due to ill health, was to have a short reign. He was 31 at the time of his ascension. Louis the Stammerer, in turn, had three sons and his desire was to insure their succession. His sons were Louis III, Carloman and Charles III (the Simple).
 

Map: The Partition of 880

Two of his sons (Louis and Carloman) were crowned in 879 after his death and west Francia was partitioned in 880. The third son, Charles III was too young to be considered an active ruler, given the needs of the kingdom. The accompanying map represents the division of Western Europe after the partition. The new kings did not have easy (or long reigns). They faced three particular challenges:

1: Their cousin, Louis the Younger, son of Louis the German, had designs on some of the Lotharingian lands CB had acquired,

2: Boso of Provence revolted and sought to create his own kingdom in Provence, and

3: Viking invasions continued to plague west Francia.

Louis III and Carloman might have made good and effective rulers had they lived, but both died young. They had been successful in defeating Viking groups and showed good command ability. But Louis died as a young man in 882 and Carloman died two years later. Louis the Stammerer’s third son, Charles, was still too young to be considered for the throne in west Francia.

Instead, the nobility turned to another Carolingian, Charles the Fat, son of Louis the German and brother of Louis III (himself now dead – 882). Charles the Fat started his reign in the west with diplomatic and military success against the continued Viking incursions but ultimately was deposed by his nephew Arnulf in 887 for failing to stem the Viking threat.

Charles the Bald or Charles the Fat:  AR denier, 21mm, 1.50gr. Obv: +CARLVS IMP AVG, central cross. Rev: +BITVRICESCIVI, central monogram. Mint is Bourges. Eudes also had coinage from Bourges.

The story continues with Eudes and the Seige of Paris.

Sources (see References for the full citation):

Bunbabin, J, France in the Making 843-1180

Guizot, M., Collection Des Memoires Relatifs a l'Histoire de France

Nelson, J, “The Frankish Kingdoms, 814 – 898: The West,” The New Cambridge Medieval History, Vol. II

Riche, P., The Carolingians