I'm not sure how much there is to be said here. The Latin for the kings we call Clovis, for example in Gregory of Tours' Historia Franconum, is "Chlodovechus." For Louis the Pious and so forth, we have "Ludovicus rex" and so on.

As far as the Anglicization (or Germanization, etc.) goes, in medieval that tends to be a question of when a figure became prominent in scholarship. It used to be the vogue to Anglicize or modernize everything, or to use a common denominator term--Anglophone scholarship still uses "Charlemagne," for example, but Germans say "Karl der Große". More recently, however, you'll often see at the front of books a notice something like "Where scholarship has used a conventional name, I continue this practice. Otherwise, I have stayed close to the primary spelling observed in contemporary records." So you'll find borderline cases like Margaretha/Margaret Ebner or King Jaume/James, where some scholars use one and others use the other. Since big-name Frankish kings have been in historiography for a long time, we get nice "palatable" versions of their names.