During the 8th and early 9th centuries, Francia and large expanses of modern day Germany were ruled by the Carolingians, which I assume means that at least the Frankish nobility shared a common language. Why then did French evolve into a Romantic language, while German became very - well - Germanic?
You appear to be confusing "Frankish", which was likely an ancestor to modern Dutch, and "French", the modern evolution of Gallic Vulgar Latin. German and French are both Indo-European languages but they are far down separate branches. It doesn't really make sense to say they split from each other.