Wow! This question is actually a lot more interesting than you realize! West Francia was always the basketcase of the Carolingian kingdoms. It traditionally had weak, ineffective rulers and was sort of a Wild West where any strongman with a big enough band of criminals could make himself into a count. The constant viking raids also didn't help, it's hard for a king to gain legitimacy when he's bribing pirates to leave his cities. France continued to be a wacky garble of shifting alliances and vassals until the Hundred Years' War, which is why its so fascinating that it became such a powerful, unified country thereafter.

East Francia, meanwhile, became the HRE because it was powerful and relatively unified. Otto I was its king and also controlled the Kingdom of Italy through marriage. He put down several revolts and beat the Magyars so bad at Lechfeld they decided to settle down and become Hungarians. He became so strong that the Pope looked to Otto for protection and thus crowned him Holy Roman Emperor, at that time a traditional practice for whichever king was keeping the pope in power.

But anyhoo, on to your question. There are a variety of reasons we could consider as to why France became a unified powerhouse and the HRE didn't. Perhaps it could be attributed to cultural differences. The French had a Roman Imperial history while the Germanic tribes were very strongly independent. You'll see a permanent preference for elective monarchy in Germanic areas, it was nigh impossible to get them to agree to hereditary monarchy.

Another approach would be to look at the critical 16th-17th centuries, where the modern state was built. The Holy Roman Empire was fragmented by religion and no leader was able to truly unify the leaders of it like the French kings had. In fact leaders in the HRE might have more interests in common with the empire's neighbors than the Emperor himself. So while France, with its hierarchical traditions, had a relatively stable state with boundaries that had been established, if not respected, for centuries, the Germans were fighting among themselves. Things like the 30 Years War divided the HRE, so while other kingdoms were building their bureaucracies and tax systems to fight other powers, the Roman Emperor and his vassals were doing it to fight each other. This is really important, because you can see the rise of the modern state coming out of these wars and their leaders' ever expanding quest for the money to pay for them.

I can't really give you a solid answer for why the HRE turned out the way it did, because I don't know myself. But if I were to do research like you these points are where I would start at.