What external/internal challenges did the Normans and the Capetians face once they took over?

The Normans faced many challenges within their own courts as originally dukes tried to have absolute power of the area and split it up into their own states. They greatly limited the rights of the people. This Norman society was taken over by the Normans of England who introduced Norman feudalism with kings as the main rulers instead of dukes. In both kingdoms the court faced great pressure from citizens wanting to go on their own independent paths at the expense of the kings. They faced external pressures from each other as the Normans tried to expand and the Capetians fought back.