Why did the western half of Charlemagne's empire become a single country (France), well the eastern half (Germany) turned into a huge group of small states?

You might be interested in some previous threads comparing the kingdom of France and the Holy Roman Empire:

Comparing the Kingdom of France and the Holy Roman Empire

Why did the Holy Roman Empire become a decentralized patchwork of states while France became a centralized, unified kingdom? - 43 comments, over 6 months old.
This post mainly concerns itself with the foundation and development of the HRE with nods towards historiographical debate.
Why did France (West Francia) end up more unified than the rest of the Holy Roman Empire (East Francia)? - 12 comments, over 1 year old.
The commenters here draw attention to the similarities between the Kingdom of France and the HRE in the Early Middle Ages.
Why did the Holy Roman Empire end up so decentralised in the first place? - 5 comments, over 1 year old.
Despite the title, the commenters in this thread mostly discuss the centralization of France while contrasting it to the fracturing of the HRE.
Why did the French kingdom become much more centralized than the Holy Roman Empire? - 7 comments, over 1 year old.
The commenters here give a discuss the centralization of France in the High Middle Ages and the fracturing of the HRE in the same time frame.

Centralization and the Holy Roman Empire

Why did the Holy Roman Empire have such a decentralized government? - 6 comments, over 2 years old.
On the HRE as an imperial institution amongst Early Modern absolute monarchies.
How did the Holy Roman Empire become so decentralized? - 5 comments, over 2 year old.
The comments are very brief but link to many books for further reading on the subject.
Did the Holy Roman Empire fragment from its original state, or did it just remain fragmented while other states centralized? - 4 comments, over 1 year old.
The comments briefly summarize the state of the HRE in its final centuries.

General Holy Roman Empire

I'm confused on The Holy Roman Empire - 6 comments, over 2 years old.
The commenters provide a general summary of the HRE at its foundation and into the Middle Ages, with some discussion of it as an imperial state.
How did the German Principalities of the Holy Roman Empire obtain such crazy borders? How were they administrated? What did they mean for a common person or even wealthy merchant in the Holy Roman Empire? - 76 comments, over 4 months old.
This covers a variety of topics from the free cities and general decentralized nature of the HRE to the life of merchants and putting it all in context within Medieval Europe.