That's the generic term used in most commonly available sources in English; that's the name people use in a casual reference. He was as French or German as a Mercian Saxon peasant in the IX century was English - in other words, not much from their own point of view. Nationalism proper is quite a recent invention.
I understand where you are coming from, of course.
But actually, I would suggest it is your concept of a "German" as being merely a citizen of a certain nation in Europe that is quite the recent invention. For instance, in 1150 they would not know of the nation "Germany" for many hundreds of years, but people called themselves Germans - although, as you probably realize, they did not use the english term for it, nor the french, which both confusingly derive from specific Germanic tribes.
You see, it is an ethnicity as well, something largely defined by language, culture and DNA. One thing I might add is that nationality as a defining point for being German has historically been far less considered than for many other nations, compared to ethnicity. Germany, as the nation, unified late, and slowly. In fact, at least as recent as the embarrassment of WW2, there were
still people outside of the
nation Germany that were considered Germans and called themselves as such.
If you had asked Wolfgang Amadeus Mozart if he was a citizen of Austria, and if he was a German, he would have answered yes to both questions, and probably sealed the deal by following up with a
poop joke. (Sorry, couldn't resist.)
So, yes, nationality is a recent invention. "Charlemagne" was certainly not a Frenchman. Did he lay the foundation for France to exist? Sure, and in that sense he is a part of founding french history. But the sense in which I say the Franks were Germanic and Karl the Great was a German is in a much older and real sense than abstract modern concepts of nationality.