To answer the genealogy question – There is considerable evidence that there was a Jewish principality in 9th century Languedoc centered on Narbonne. Contemporary chroniclers have written about it and our own sources, like Binyomin of Tudela writing a few hundred years later describes Narbonne as where the “zera hamalchus” resides when he meets the community’s leaders.
The family of the leaders of this principality, descended from someone named Machir of Narbonne, might coincide with a branch of the family of the Resh Galuta in Bavel being exiled in favour of another branch (see Otzar Hagedolim on the R’G Natronai II) and traveling from Bavel to this part of the Jewish world, as is described in some sources (For this you will have to read the very hard to find “A Jewish Principality in Feudal France” by Columbia U professor Arthur Zuckerman).
Eventually some of the descendants of these leaders assimilated, particularly the descendants of Guillaume De Gellone, of the family of Machir, though he himself apparently did not. These descendants married into several royal families of Europe, including the Boullion family who became “Kings of Jerusalem” during the Masaei Hatzlav, who eventually became the house of Anjou (Think Richard I), and whose descendants are all over Europe today including the British royal family.
From our Jewish perspective, there may be some further support for some of this narrative, including more snippets and fragments from Jewish travelers and from Rabbinic genealogies, and the family of Rav Shmuel Ben Natronai, the Rishon from whom the Margoliyos family ultimately descended, also came from this area of Languedoc, and the name Natronai is clearly from Bavel and exceedingly rare among Ashkenazi Jews. (I have only found it twice among Rishonim, and this is one of them)