It can be hard to grasp how decentralised and fragmented the early Medieval French Kingdom was. We tend to, in a post Westphalian political world, view historical kingdoms and empires as cohesive states with clear borders and a functioning sense of sovereignty and governance.

This couldn’t be less of the case for medieval France in 1066. The King of France in 1066, Phillip I, based in the rich but comparatively tiny demesne of the Ile de France (areas around Paris and a patchwork of lands to the north and south) could count on little support or even loyalty from the powerful Dukes and Counts who surrounded him and made up the nobility of France. While he was nominally the man they owed homage to, and had advantages in terms of his relationship with the Church (no small thing), his effective power often ended at the borders of those lands he directly controlled.

There are numerous examples to illustrate what I’m talking about, but let’s take a quick area scan to see what was going on. To the King’s east lay the lands of the Counts of Blois/Champagne, a powerful family that often took to raiding their neighbours and even the Kings lands. To the west and north lay the burgeoning power of the Dukes of Normandy, as you mentioned - at first a settled population of Norseman tasked with guarding the northern approaches of the Seine from other marauding northmen, but who eventually gained more lands and set themselves up as a practically independent feudal state. To the far west the counts and Dukes of Brittany ruled a land that was geographically, linguistically and politically very remote from the Kings court in Paris - they belonged to a northwestern sphere of influence that made their connection with England and Normandy often of more importance than that of France. To the far south lay the powerful Dukes of Aquitaine and Counts of Toulouse - essentially independent lords who owed only nominal fealty to the King.

That’s not all to say the King was powerless. His rich demesne (personal lands) and strong base in Paris gave him wealth and prestige, and his connection to the Church was important and crucial to his reputation. But his role often was as an arbiter in debates and confrontations between powerful vassals, not that of a despotic ‘l’etat c’est moi’ type monarch. Kings of France would need to be crafty and dogged in their fight for domination over the far flung lands of the ‘Kingdom of France’ - and doggedly crafty they often were.

So the best answer to give on your question is that when Duke William set sail, there honestly wasn’t much the King could do. William had built a military machine during his reign that was probably one of the finest in Europe - he had alliances that brought Flemish and Bretons and Frenchmen to aid him, and his lands of Normandy were rich and closely guarded with a dense network of castles. His claim to England was also supported by a Papal Bull, and in 11th century Europe that was about as airtight as you could get.

One opinion I’ve seen was that part of William’s motivation in taking England was to put him (feudal rank wise) on the same level as the King of France. The two quarrelled often, and the lands along the Seine in what is known as the Vexin would be a point of conflict for over a century as their successors battled over the rich lands between Rouen and Paris. So having a Kingdom to call his own would give William a much better elevation to dispute with his rival in Paris than if he was an even functionally independent Duke.

It should always be taken into account that the Norman and Angevin monarchs always spent more time in France during their reigns than in England - at least until John. England was (comparatively) a backwater until the late Middle Ages - the continent and connections to the Mediterranean were where the wealth, power and prestige lay.

But your question is a good one - the next four hundred years of history would be a continual tug of war between the two entities, much of it revolving around the ultimate question of fealty. Was King William responsible to King Philip for his Dukedom of Normandy? Who was superior? What position were minor vassals in, if they were technically under both authorities? All of these questions would result in bloody conflict for centuries to come.

Some good broad sources for the period I can recommend are these:

Tout, The Political History of England, 1216–1377 (1905)

Barlow, the Feudal Kingdom of England, 1042-1216

Prestwich, Plantagenet England, 1225-1360 (2005)

Prestwich, Michael (1997). Edward I

Trevelyan, G. M. (1953). History of England.

Book, Christopher (1963) The Saxon and Norman Kings