Like Elfwine, I'm not sure Philip Augustus would try to conquer Gascony: I think he was already satifsied with having recovered 3/4 of the former Plantagenêts holding. Another thing that comes to my mind is that he had the chance to send reinforcemnts to his son Louis when the latter tried to seize the English crown from John Lackland (with agreement of the Barons at first). But Philip Augustus never did such a move: he was probably satisfied with a weaker England and no more "Plantagenêt Empire".
On the other hand, I think Louis VIII might have tried to size Gascony if he had lived longer, after he had dealt with the Albegiesan Crusade. If I remember correctly, Louis VIII was pretty pissed that the English Barons had let him down and also lead a few raid in Gascony when he returned from his expedition in England. Plus, Louis VIII does have a weak claim to back an attempt at seizing Gascony.