It would not be fair for me to speak on behalf of the French/West Francian experience, but as far as Germany goes, the answer is no.

For starters, there were four major kingdoms definitively established in western and central Europe from the Treaty of Verdun: West Francia, encompassing much of modern France, East Francia, encompassing most of modern Germany, Italy, which took up the majority of the Italian peninsula and shared borders very close to the modern borders of Italy, and Lotharingia, a state caught up between West Francia and East Francia, including the Lowlands, modern Switzerland, and a relatively thin strip of territory between them.

Lotharingian land became a source of much contention between several European powers from the Treaty of Verdun onwards. The Burgundian Succession, for instance, was one such example. Another example was the Treaty of Ribemont, where Lotharingia itself was divided up by the other Carolingian kingdoms. This land never gained a national identity, instead fracturing between German and French cultures over the millennia of violence fought over it.

East Francia DID NOT become Germany. When the Holy Roman Empire was recreated by Otto I, he was considered the king of Germany. However, this kingdom was heavily decentralized, and people identified themselves with their feudal overlord than their king, or their Emperor, when the HRE was formed again. When the kingdom title became elective in 911, division into separate “states” inside the Empire was guaranteed. There were intense divisions between Holy Romans in Austria and Holy Romans on the border with Denmark. Holy Romans in Bohemia, between both of these geographic groups, spoke Czech, not German. Economic bases were completely separate in these varying parts of the Empire, and where Austrians had gold, Pomeranians had Baltic fish. Simply put, the only people who ever wanted to make the HRE a proper, centralized, unicultural state in the modern sense were Emperors themselves, and even then, emperors who would have wanted that were few and far between. Asking why the HRE never became Germany is asking why Italy never became German: It was never intended on centralizing.

The Protestant Reformation threw a much stronger wrench into any idea of German unification, with religious division becoming not just more intense, but much, much bloodier. The southerners, like Bavarians and Austrians, held to their Catholic belief, sharing their closeness with the Papacy and their even more Catholic Italian neighbors in the Empire. Northern Holy Romans did not share this warmness and closeness, and did not hold the same trust in the Pope’s word that their siblings of the south did. The printing of the Bible for all to read was something the northern Germans began to cling to very strongly.

So, what changed? As with many questions of Europe between early modernity and today, the answer is Napoleon, or, more accurately, the French Revolution.

The French Revolution was truly terrifying to the European kingdoms and the Emperor of the HRE. With the defeats from the first of the coalitions, the Emperor encouraged minor states to merge with their larger neighbors. In many ways, this was an Austrian power play to consolidate power on all of their lands, allowing for them to unify all their South German land cleanly into a “full” Austria. However, this had the same effect in North Germany. North Germany had many more minor states and city-states, and they, instead, merged into Prussia. The 1806 destruction of the Holy Roman Empire was attributed to Austrian weakness, causing even further resentment in northern and western Germany. The German Confederation formed to protect the minor states that remained, with Austria conveniently being in a weaker state than when they were Emperor. Prussia could easily consolidate power, and, with the rise of nationalism in the 19th century, German nationalism, not Prussian nationalism, was finally born.

Sources: Peter Wilson’s Heart of Europe and The Thirty Years’ War