After William the Conqueror became William I of England, tensions began to rise between the Duchy of Normandy and the Kingdom of France.
As Duke of Normandy, William was subservient to Philip I of France, but as newly crowned King of England, he was an equal of Philip I.

The Kingdom of England became a Norman possession more so than Duchy of Normandy became an English possession - this is the case in William the Conqueror’s time, but it was to change in future generations.

Following William the Conqueror’s death, the Kingdom of England and the Duchy of Normandy were bequeathed to different heirs of William.
William Rufus (3rd son of William) succeeded William as king of England, and Robert Curthose (1st son of William) succeeded William as Duke of Normandy.
After the death of William Rufus, Henry I inherited the Kingdom of England.

There were attempts to bring the Duchy of Normandy under the control of the Kingdom of France, but they were repelled by Henry I, who subsequently made the Duchy of Normandy an English possession.

During Henry I’s reign, Ireland was invaded by a force of Anglo-Normans and Cambro-Normans, and was added to the Norman territories under the King of England. It was technically a Papal fiefdom (Henry I conquered Ireland on behalf of the Pope).

After the Angevin succession to the English throne, tensions grew stronger again. The Angevin kings of England held vast swathes of territory in France (such as Anjou), and posed a threat to the Kingdom of France. It was therefore French policy to conquer Angevin lands in France and incorporate them into the lands of the French Royal Demesne.

The Duchy of Normandy was eventually acknowledged by the Angevin kings to be incorporated into the Kingdom of France following the period of Anglo-French wars that ended with the Treaty of Paris (1259).

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More can be said, but this might be a good start for you.