How were the French Capetians able to overcome the much wealthier and more powerful Plantagenets?
Most interestingly, the Capetians/French were unable to take these territories during the anarchy of the decades long civil war between King Stephen and the Empress Matilda, what changed to allow them to take advantage of a series of relatively more minor civil wars?
Just a small correction of your timeline, Stephen and Matilda were Pre-Plantagenet empire.
There was the duchy of Normandy tied to the English royalty but it was held in homage to the French Throne and there was no need for the French Kings to seize it.
Matilda married Geoffrey of Anjou, The Plantagenet. Tying Anjou with Normandy and England.
Their son Henry II ended the Civil war and Married Eleanor of Aquitaine and took over as Duke of Aquitaine, Duke of Normandy and King of England.
It's under Henry when the conflicts with the French throne begins because through right and marriage Henry gained half of France and began throwing around his influence