I personally think the best starting point is Frederick Cheyette's Ermengard of Narbonne and the World of the Troubadours. Despite the title, it's actually a pretty in-depth introduction to Occitan society, politics and culture, covering most of the twelfth century (and a little of the late eleventh). It's clearly written, grounded in the primary sources and a fun read. It's not perfect, of course: Cheyette was one of Peggy Brown's best friends, so he protests a bit too much that "these complex hierarchical relationships aren't feudalism, I swear!" and his footnotes are all at the back of the book, which is a bit of a pain when you want to look things up, but overall I think it's a very good start.

It can be supplemented with the relevant sections of Dunbabin's France in the Making (where she focuses mainly on the Rouergue and Toulouse, IIRC), the chapter on Occitania in Marcus Bull's France in the Central Middle Ages and the relevant chunks of the New Cambridge Medieval History, vols 3, 4 & 5. All of these works have got ample bibliography, but if you're looking to dive head-first into 600+ page specialised regional monographs in French, I can also recommend a few!

For readability, synthesis and being English language, Fredric Cheyette's Ermengarde should be one of your top two entry points. The other is John Hine Mundy's Liberty and Political Power in Toulouse 1050-1230 - it's far broader than the title suggests. I would council reading it first, including the incredible footnotes, before reading Ermengard.

French, Anglo and German historians alike refer to Mundy's career-long focus on Toulouse and regions as a touchstone in scholarship. He spent decades in the archives of Toulouse - his introduction to his last book Studies in the Ecclesiastical and Social History of Toulouse in the Age of the Cathars gives you a real sense of what the state of mid-20th c archival work was like (the use of 'Cathar' in the title was a marketing ploy by the publisher).

These two books by Mundy and Cheyette together will give you a real sense of being in these worlds, and at the same time you'll see a contrast of how these two important southern communities functioned viz. their times. Through these two books you'll see every 'issue' we discuss here about high medieval society reflected and refracted (...and as an added benefit, neither author needed to use the term 'feudal' :) ).

To reverse your question, what are some books you would recommend to understand northern France in the middle ages?