aquitaine came into english possesion, as monkeyman said, by the marriage of henryII and elearnore of aquitiane. can't give you the exact date, but it was around the early 1200s/late 1100s.

anjou i'm no sure about. but at this time, the feench throne as it was had fairly nominal control over france. powerful and often warring duchies ruled france. brittany and Normandy being 2 of these, places like Lorraine, and Alencon and gascony (aquitaine) as well.
these duchy's i believe came about as a result of tribes within the frankish nation, such as the normans. with the normans gaining the english throne, i think the french unoited under 1 leader... to oppose them gaining control of france as well, the normans being very powerful.