Charles 'the Younger', King of the Franks - Birth Place Mélange

Medlands posits [Aix-la-Chapelle] aka Aachen as a its guess for birth.
Are there respected sources that support Cologne or Köln for birth?
Rhineland as "a loosely defined area of Western Germany along the Rhine".
If one accepts Aachen as Charles' city of birth, the Rhineland should appear second.

Three regions in the place-name strand are historically invalid:
1. Germany founded on 18 Jan 1871. Until then, "Alemannia" was the was oft used Roman name beginning ca. 213.
2. Prussia comes into existence in 1525.
3. Nordrhein-Westfalen becomes an operational region on 23 Aug 1946.