They are the same people as those from the north ethnically, the difference is more cultural than anything and even then it's quite slim nowdays.

The population of modern day France didn't change much in it's ethnic make up throughout history. The local Gauls were already 9 to 12 millions according to Eugène Cavaignac's estimations. That's already a huge population, especially for ancient time, and so Roman and then Frankish conquest were not a replacement of this Gallic by what were essentially minorities but a settlement that simply mixed with them in the following years.

Saying that specific regions of France are descendants of specific peoples is just false historically speaking. If you were to look at your family tree that far into the past it would be massive since it dobbles in size each time you go back a generation. In fact family trees are so large that mathematically they are more entries in a family tree than they are people who ever lived on Earth, which is explained by the fact that some people appear several time in family trees because of inbreeding.

So any French person would have Gallic, Roman and Frankish ancestors aswell as from other parts of Europe for sure.

Now culturally they are, or were, differences. Occitania is a part of southern France which had a it's distinct cultural traits for centuries. As part of the langues d'oc family, the language is related to modern french which comes from the langues d'oïl which are from the north of France. So the two are from related but distinct family groups, related as in gallic evolution of vulgar latin.

In general Occitan culture, especially in medieval time, tended to be more roman like than it's northern counterpart which were more germanic in influence. For example in northern France the leader of a city or town were called "échevin" which comes from frankish, while in southern France they were still called consuls like in Rome. The southern part of the kingdom also had it's own estate general, or assembly the king could call for important decisions, distinct from that of the north.

Though in modern times the differences between the two have largely been reduced. The French Revolution abolished any special laws or treatment regions could have, French people from all across the country left their home region and moved to work in city where they mixed, and parisian French became the standard. Although not a dead language Occitan now only count around 500 000 speakers, varying depending on sources. Most of them are in southern France but they are also some in Catalonia and north-eastern Italy.

There's a little problem in your question. Though some scholars define the Occitans as an ethnic group, they are mostly called as such because of the dialect the speak, "la langue d'oc".

"Oc" means yes. In Northern France, people said "oïl" instead, which later gave the modern French "oui". However, Southerners and Northerners spoke the same language: French. No surprise there, French is only Latin that kept on being spoken and changed over time. Though French appears like quite a unified language nowadays it wasn't so in the past. It was divided into plenty dialects which gathered into two families according to the way they said yes, "oc" in the South or "oil" in the North.

What happened?

Basically, there were people long ago that built menhirs and such and there isn't much we can say about them before the Celts migrated into Gaul and became the "Gauls" as the Romans called them.

Southern Gaul was soon tied to Rome. It'd been where the Greeks established colonies like Massalia. Southern Gaul was therefore more in touch with the Mediterranean trade where, eventually, the Romans prevailed.

This Southern region of Gaul became known as the "Provincia" and one of the very first regions attached to the Roman Empire outside of Italy. Latin prevailed long term in the administration and in business in that region and it did for a long time before Latin was picked up by the Northern Gaul regions. Thank you, Julius Cesar. This had as consequence that the Occitans, in the Middle Ages, spoke a French dialect that was much closer to Latin than their northern neighbours.

When the Wisigoths, the Burgundians and the Franks conquered Gaul, they changed little to nothing to the Roman administration still in place. Latin remained the "lingua franca" and they learned it over time. We can't say, therefore, that the Occitans migrated from any place or other. They were the inhabitants of Southern Gaul were Latin was better spoken than in the North.

Fun fact, however, the Franks made Paris into their capital. By the 11-12th century, somehow, the people of Paris (the royalty, especially) were convinced to speak a better and nobler French than their neighbours, though major works of French litterature had been written in other dialects at this point.