Well, without the Albigiensan Crusade, the Counts of Toulouse will probably remain independent and won't have to worry about Northern nobles invading. Peter II of Aragon will also not be killed during that Crusade, as will Raymond Roger of Trencarvel, viscount of Carcassonne.
The three families of Carcasonne, Toulouse and Aragon (which held a number of counties like Roussillon) were the dominant ones in Occitania: there was no unity.
There was a feudal unity, nevertheless, Trencavel dynasty was vassal toards the raimondine one (except for Razès) and the counts of Tolosa never neglected to have a better hold on these lands. In fact, it's why they joined the Crusade (it half-worked, as they can take lands from Trencavel's at the Treaty of Meaux).
So there's room for a Tolosa growing grasp in Mediterranea.
Aragon have lands in western Occitania, but mainly as vassals of Tolosa (except for Montpellier), so it's not really a big deal.
Where Aragon is more important, it's in Provence that was a barcelonese inheritance.
Without the Albigensian Crusade, I guess you would still see competitions between them. Particularly between Aragon & Toulouse because the latter shares a long enmity with the Counts of Barcelona (which has been inherited by Aragon). Furthermore, the Counts of Toulouse were rather close to Castille if memory serves me right.
Not really that close, Dukes of Aquitaine were more.
Regarding Aragon, in fact they have a rather acceptable attitude. Not only Aragon was vassal of Tolosa for Gavaudan, but they had a common competitor : the Trencavel. Again, when Raimond VII searched an ally, he asked for Peìre II of Aragon.
I do not see why Occitania would join Italy: it's not near the Alps and there were few interractions between Toulouse and Italy.
You're aware that
1)Occitan is actually spoken on the two sides of Alps
2)
The Count of Tolosa had lands on Provence
?
Aside from the Pope which eventually inherited Avignon from Toulouse
Actually, Avinhon was not a possession of Tolosa, when the Pope took it. It passed into Anjou's lands and the city was already autonomous since the XI and even a republic for sometimes right after the Crusade.
However, I believe there is still a good chance that Toulouse keeps interacting with France. For one, they could share a common ennemy in the Plantagenêts: there is a long feud between Toulouse & Aquitaine and Richard Lionheart had forced Toulouse in vassalage.
It was a sport among the dukes of Aquitaine anyway, and not really griefing.
In fact, the Tolosan supported everyone that NOT tried to limiting their power.
You have far more odd indeed that Raimonds continue their ties with Capetians, not because of a common ennemy (in fact, making royal armies come in the south would increase the power of the king) but just because it was a far presence, not forcing him in any way.