Like Captain Frakas correctly stated the term frankish lost it's ethnical meaning at least one century before charlemagne and could refer to the noble of old frankish descent as well as the romance burgher in Neustria or the low german in modern belgium (proto-dutch) and even the high german in rheinland (franconian).
3. Charlemagne was the first king in Europe since the collapse of the Roman Empire to become king of two peoples and to style himself as such (king of the Franks and of the Lombard). As far as I know, there is no king who styled himself as King of the Franks, the Burgundian, the Visigoth, the Normans, &c.
I was thinking after Charlemagne, I have a hard finding the exact source where I found this .
But I at found that at least some of the kings of franks added in their title king of the Aquitaines as shown here:
http://fr.wikipedia.org/wiki/Liste_des_ducs_d'Aquitaine (french only) after the integration of the kingdom of Aquitaine in the Kingdom of France.
So for me it confirms that the occitans were not considered franks like the their northen cousins as for the other ones i guess that it's not a big stretch that it could have been used too but I keep looking for evidence.