There are two answers to that question, both equally true. I’ll try to explain that a bit, but keep in mind that my specialization lies in late medieval France and, even though I may conjecture a bit about earlier power struggles, it should be taken with a grain of salt. Anyway, let’s get going.

The first answer would be: « Not that easy to do, m’lord ».

It is important to keep in mind that medieval kings (and especially English kings) were not at any rate absolute monarchs. They relied on the support of nobles, administrators, bourgeois and the population in general. I’ve elaborated a bit in the past here on that subject, if you’re interested in more details, but if we go back to your question, that meant it is not enough for the king to declare their French holdings part of the Kingdom of England. For it to be effective, he would need the support of local population and elites.

Remember that, as holders of titles in Normandie, Anjou, Guyenne etc., the kings of England were vassals of the king of France. That meant they pledged their allegiance to the French king. A limited one, of course, that is limited to specific lands and all, but still. Now, the Normand barons for instance, swore a double oath: to their duke, and to their king (i.e.: king of France). Nothing guarantees that, should the king of England declare Normandy part of their own kingdom, the barons would follow. The opposite could be expected: their oath to the king of France tops their oath to their duke. Same goes for non-noble elites. Therefore, declaring it would not be enough. He would need local support. As an example, when Richard 1st of England is captured in 1191 on the way home from his crusade, French king Philippe Auguste plans an invasion of the Normandie. Learning about it, John, brother of Richard, lands in Normandie but the local barons refuse to recognize him as their liege and to swear their fealty to him. He has no choice but to kneel before Philippe Auguste.

He would also need to be able to enforce that separation from the kingdom of France. Making sure taxes are paid to his Chancellor of the Exchequer, and not to the French administrators, for instance. And you can imagine how that would be harder for an English king in London (or whose administration is mainly concentrated in England, at least) than for a French king in Paris. The farther you are, the harder it is to control and administer a province. And even if local elites supported you at one given moment, that does not mean they will keep doing that if they feel too much tax pressure. Or if they feel the English king intervenes too much in their affairs. It is easy for them to go and moan to the court of France, claiming to be persecuted or abused, because they know they will be well received.

That leads to our second answer: « Oh, but they did. Or they tried to ».

The question of the sovereignty of the French holdings of the English kings has poisoned the relations between the two countries for centuries. So much so that it is, in fact, a major cause – or even, the major cause – of the most famous European medieval war: The Hundred Years War. One can notice that, for instance, Normandie and Guyenne were very contested zones. When it came to war between France and England, those provinces were generally disputed territories. See Richard 1st for instance, who built Château-Gaillard to protect his possessions in Normandy. But France wasn’t an easy prey, and the French kings were not willing to part from their possessions. The Normandie was for a long time a cause for war, and it eventually led to its conquest by France. Château-Gaillard is captured in 1204 and the rest of Normandie follows suit and, despite other military operations, it stays French. Something confirmed by the treaty of Paris in 1258.

The Hundred Years War, though, is the last argument, the last battle fought over the possession and sovereignty of the French possessions of the kings of England. As I said, this question is one if not the main cause of the war, but we will need a bit of context.

The treaty of Paris of 1258 confirmed that the Normandie was returned to the king of France, but it also confirmed that the duchy of Guyenne (or Aquitaine) was held by the king of England. It specified, though, that the duchy remained in the kingdom of France and that the kings of England would therefore swear their fealty to the kings of France for that duchy.

At the time, it was a compromise to end a war and find a solution that could satisfy everyone. One century later, it had become insufferable. The English kings became more and more reluctant to uphold their duties regarding their liege, especially regarding all things related to fealty, allegiance and oaths. They dodged convocations, pretexted sickness, etc. They did not want to swear any kind of oath and did so reluctantly when there was no other choice. Philippe V of France had to wait two years for any oath, and it was not said in person but by representatives. Edouard II of England only accepted to come himself one year later, and only because his county of Ponthieu was occupied by French administrators until he would come and swear in person. The French kings were not better: quick to try and erode their vassals’ rights and prerogatives, uncompromising when it came to punishing offenses (real or amplified) from the local population against the rest of the kingdom, happy to sow discontent among the local nobility and to take advantage of their divisions and their bitterness about the English kings.

Thus, when Edward III became king of England in 1327, the situation was tense. Keep in mind that, in the last 30 years, the duchy of Guyenne had been confiscated twice! To make the matter worse, he had a decent claim on the crown of France, arguably stronger than the current French king (however, since the strength of the claims depended on an unprecedented event, there was no clear rule for that precise situation). He knew very well that the council of French barons would not support him: he was not a « stranger », being the grandson of Philippe le Bel, but he was a Plantagenet, and therefore king of England and heir of a line of turbulent vassals. He knew, however, the weight his claim would have when demanding that the Guyenne be reattached to his kingdom of England. A proof can be found in the second treaty of London following the disastrous battle of Poitiers of 1356. The king of France, Jean le Bon, has been captured. The French nobility has been decimated. The person in charge is the young Charles, future Charles V, son of Jean, who has to deal with rebels and struggles to keep the control of the situation. But does Edward III demand the crown of France? No. Even in his most triumphant hour, he « merely » demands the whole sovereignty over the Guyenne (and a couple other counties and duchies of course). His goal was to make his French possessions (and conquests) part of England and to end his bastard position of king and vassal.

To sum it up: the kings of England did try on several occasions to make their French holdings part of their kingdom, but it wasn’t that easy at all. The opposition of local populations taken in a crossfire of feudal obligations and oaths was an obstacle, but the major one was of course the might of France, which did not intend to let it go as easily. Wars were fought on that very question and, although it took some time, it eventually led to the English kings losing all of their French possessions, save Calais for some time.

I hope that answered your question, feel free to ask any more detail or precision!