No, Charles and the derivations are not "original English" but went through a Romance tongue. The modern English to expect would be either Carl or Charl, but not Charles ("blame" the Norman nobility for that).
We are Germans full stop, not "Germans in a sense". That'd be like saying the Flemish were Dutch "in a sense" or that the Asturians were Spanish "in a sense".
It is just very transparent, but I'd be careful with tracing it to any other country. It is just a very transparent surname, coming from a Germanic word that has cognates left in every Germanic tongue. Even the surname is pretty much omnipresent also in German: Traudl Junge, Hitler's secretary; or Carl Jung, the famous psychiatrist (his paternal line was unquestionably Swiss-German).

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