Louis is indeed derived from Clovis, which itself is the francicized version of the Germanic name Hlodwig which is Ludwig in modern German. In France, the name Clovis changed to Ludovic, then Louis.

Apart from the fact that Clovis and Louis look and sound different, what makes the separation in terms of numbering is how these names have been latinised on official records. Kings named Clovis were latinised as Clodovicus, and from Louis I on that name was latinised as Hludovicus or Ludovicus.