This is a what-if I've been musing over from a wargaming perspective (so I've tended to presume events proceeding in a way to provoke conflict), but I think it's a potentially interesting POD even if none of that materializes.
Louis VII dies in 1180 with one son and a handful of daughters. The POD is that, when he dies (basically right on time), he doesn't have the son. This could be either by presuming Philip was never born and minimizing butterflies afterward, or, perhaps more reasonably, by assuming that Philip dies a few years before his father does in some kind of accident.
In 1180, as far as I have been able to discern, the French king was still nominally being elected by the nobility of France (nominally in that they had spent roughly the past 200 years electing Capets). There was, at the time, not yet a precedent of having only male kings of France (though the Anarchy in England might be fresh enough in everyone's memory to push them in that direction).
My reading has pushed me toward what I believe to be the three most likely candidates to take the throne after Louis:
Robert of Dreux was Louis' eldest living brother. I don't think he held any particularly impressive holdings, but he had at least one son, he was a male Capet, and both he and his son seem to have done some substantial campaigning in their lifetimes. I don't know that he had anything outstanding pointing to him, but he might have been a strong compromise candidate.
Henry of Champagne was married to Marie, Louis' eldest daughter. Champagne was enough, as far as I can tell, to make him a powerful magnate in France. Beside that, he had numerous siblings in powerful positions, including a brother who was Archbishop of Reims. He and Marie had a young son (also Henry) who was betrothed to the daughter of the Count of Hainaut (and niece of the Count of Flanders) - in real life, the marriage fell through because she was instead married to King Philip. Here, that cause, at least, won't happen. Henry had fought in the Second Crusade, and Marie is purported to have had a very positive relationship with her brother Richard, future king of England. All of this would seem to amount to a substantial amount of force that Henry could muster in support of either himself or his wife.
In OTL, Henry was being held prisoner in the holy land around this time and (after being ransomed) died in 1181. That puts a damper on his prospects. Of course, if he can see a succession dispute coming up, he might decline to make that trip, and not being captured could increase his life expectancy.
Henry "the Young King" of England was married to Margaret, Louis' third daughter. Margaret was Louis' first daughter not by Eleanor of Aquitaine. While I've not seen any evidence that her sisters were ever held to be illegitimized by the annulment of their parents' marriage, I'm not sure that I would expect that to continue if the question of the French throne came up. Henry, in theory, has the backing of England behind him and his wife (England being ruled by his father, Henry II - in my head, I call this the War of the Four Henrys). Henry (the younger one) seems to have been pretty popular in general. Of course, that didn't extend to his family, and he was at war with his father only a few years before Louis' death, and would be at war with his father and brother Richard again only a few years later, ultimately dying in 1183 of illness, and never having any children. Of course, his death was, to some degree, a fluke - he certainly could have lived longer.
So, the questions, I guess, are:
Peaceful succession or conflict? If the latter, who is likely to have the edge? Are there candidates that I've not thought of?