I'm assuming then that the Gauls were Frankified eventually after unification. How does Occitania fit in here? Is it a cultural identity that evolved seperately, or is it more geographical?
Occitania seems to have been gobbled up by the Frank conquest like other areas. That didn't prevent the development of local culture though, as we can see in the map of the OP, there was a large diversity of local cultures all around the country, even with a single king ruling on all of them.
Of course the history of the different areas are more complex than their global administration, all regions were influenced by the neighboring countries, migration flows, wars and invasions...
Frank areas after conquests by Clovis 1st :
Frank areas after conquest by Charles the Great :