I think there would have anyway been a conflict between the Capetians and the Plantagenet.
The reason is quite simple. There was a deep and long trend to moving away from feudalism to centralization, from suzerainty to sovereignty. The royal power was asserting itself at the expense of the feudal power.
And when you are the sovereign king of a country that is a big power, it is not tolerable to have one of your most important vassals who happens to be the sovereign king of another big power.
Concerning France, the distance separating Paris from Normandy was but 75 kilometers. Just imagine if the king of France held the counties of Wight, Hampshire, Wiltshire, Dorset and Somerset. As soon as he becomes strong enough, the king of England is going to try to end this situation.
You will notice that, while the dukes of Normandy had long been faithful allies of the capetian kings of France, they became structural enemies quite quickly after the duke of Normandy became king of England.
Holding Aquitaine, did not deeply change the nature of the problem. It did so all the less than the duchy of Aquitaine was in fact very decentralized while the duchy of Normandy was very centralized.
It is not a coincidence if the kings of France took and retained control of Normandy as early as 1204 while they coule live quite securely for a much longer time with the Plantagenet holdings were limited to the coastal part of Aquitaine.