My gut reaction on first seeing this was to say “NEITHER!” I stick with that answer (that if you picked up Karl or any of his subjects and dropped them into modern France or Germany they would likely recognize just as little in either case) but there’s a greater complexity to your question that I want to unpack a little.

When we think about kingdoms or empires, particularly in the pre-modern past, there’s a tendency to think about them as less complex entities. When we look at the Frankish Empire of Charlemagne, we are, actually, looking at a very culturally diverse place.

At its height, Karl ruled over a huge swathe of territory comprising parts of modern Germany, France, Austria, Spain, Italy, the Netherlands, etc. Each of these pieces had its distinct cultural quirks or, indeed, a separate culture. Karl wanted religious uniformity from his subjects and was fully prepared to spill blood to see that done (ask the Saxons) but he didn’t push for any sort of greater cultural normativity, making his Empire “Frankish,” at least to my knowledge. There was no monolithic culture of the “Frankish Empire,” nor was the Frankish culture of Aachen the same as the Frankish culture of Paris, etc. The elite shared more of a common culture, but even then the expectations of a north Frankish noble from somewhere like Champagne would differ from those of a southern Frankish noble from somewhere like Toulouse. For starters, they would speak different languages - Frankish in the north and Occitan in the south.

Because of this, I don’t think it’s really possible to speak about “Frankish” culture as having strains enduring to the modern age in any but the broadest elements, such as “there are bridges and churches and people eat bread.” It’s been too long (over 1000 years) for more meaningful traces to have carried on wholesale, especially considering the pace of change over the last 100 years.

All of this said, however, we still look for those connections and they mean something to us. And digging deeper into where the questions come from can help us better understand the sorts of things you’re looking for. So, what interests you? What led to your post?