The question already starts with a wrong premises. The Franks in a certain sense became the Germans. Franks were a Germanic people, speaking a Germanic language which developed to later become the German language(s). A lot of people seem to think Charlemagne was some kind of early French king. He was not. Karl, which is the German version of his name, Charles being the French version, spoke, as did the Frankish nobility for almost the next 200 years, a Germanic language. He also was of Germanic descent, whereas the greatest part of the people, who went to become the French, were Roman-Gallic and spoke a vulgar kind of Latin.

Both territories, the territory, in which people spoke the earliest stages of German and the territory, in which people spoke vulgar Latin which slowly developed into French, were under Frankish rule.

When the huge Frankish empire therefore steadily declined and the attempts of unification under later Karolingians failed, practically 2 big (and a third, for this topic not so important smaller part) blocks developed. The Eastern part and the Western part of Frankia. The Eastern part became Germany, but also in the Western part, which was to become modern day France, the Frankish leaders still spoke their Germanic language.

The leaders adapted to the diversion of both parts of the country. The western lords soon started to speak Latin/ Early French, the Eastern Lord the early stages of modern German.

The final nail in the coffin of the final secession of both parts of the great empire of Francia was Otto being crowned Roman emperor.

Therefore, as a summary:

The Germans were not a people under foreign Frankish control. The Franks themselves were Germanic lords ruling over the Germanic tribes and their remnants in what was to become Germany and the Roman-Gallic people, in which was to become France. There was no bounding institution left, from which one of both people could have emancipated from. They simply drifted apart in an over two century long development.