The answer to your last two questions is "yes". With regard to marvelous feats, the Anglophone world knows all about Crecy and Agincourt. But we don't hear much about the Loire Campaign (1429, the French won four battles in a row and broke the English grip on central France), nor about the Battle of Formigny (1450, a small Franco-Breton force crushed a larger English army to regain control of Normandy), nor about the battle of Castillon (1453, a catastrophic English defeat that wiped out England's last field army in France and killed the English commander, at the cost of just a couple of hundred French casualties).

Going into the whole history of Anglo-Norman-Franco-Burgundian relations over almost 400 years is beyond the scope of a Reddit comment, so I'll just focus on the last bit: the collapse of English rule, slow at first and then accelerating, after around 1428.

Historians are still arguing about whether this was very likely, pretty likely, or somewhat accidental. On one hand, the English got hit with a string of bad luck -- Henry V dying unexpectedly leaving an infant son, then Joan of Arc shows up, then the Burgundians abandon the English, then Henry VI turns out to be a dithering incompetent. On the other hand, up to 1435 the English had very competent leadership under Duke John of Bedford -- Henry V's younger brother, and Regent in France for the young Henry VI. (In England the Regent was Henry and John's other younger brother, Duke Humphrey of Gloucester.) John wasn't Henry V, but he was a very competent military commander, a solid administrator, and nobody's fool. And the French had their problems too -- Charles may have been "The Well-Served", but he wasn't exactly a brilliant diplomat, nor any sort of warrior.

That said, it's notable that once things started to go wrong for the English, they /kept/ going wrong -- there's a very distinct arc to the last 25 years of the conflict, and it's steadily downhill for the English. If I had to choose a turning point it would probably be the Burgundian defection. Some historians say this happened after the death of John of Bedford, but actually it seems to have kicked in a couple of years earlier, in a dispute over John's second marriage. Trivial stuff, but it involved a snub to the Duke of Burgundy, which apparently he never forgave. Anyway, somewhere in the first half of the 1430s the English position in France moved from "long term problematic" to "probably doomed", and it never got better after that.

The deep underlying forces... sure, French national feeling was absolutely a thing. Nobody loves to be ruled over by aliens. Under John of Bedford, English rule was okay -- no worse than being ruled by France. But after he died, the internal bickerings of the rudderless English court spread to France, with dramatically bad effects on governance there. I mean, by the late 1430s England was ruled by a teenager who was obviously not up to the job, surrounded by an ever more vicious pack of corrupt and scheming nobles who hated each other. There were a few decent-ish men who tried to keep things from getting too far out of hand -- this is when young Richard, Duke of York (father of the Yorkist dynasty) starts becoming prominent -- but on the whole, English governance was a godawful mess with no obvious exit ramp in sight. King Charles started to look a lot more attractive in comparison.

On the other hand, Gascony and Normandy had been ruled by the English basically since forever. Gascony often caused problems for English kings, but that was because it was distant, culturally very distinct, and had rugged terrain that made it easy for overtaxed peasants to turn bandit or disgruntled knights to hole up in a keep up a hill somewhere. After 1453, Gascony would give plenty of trouble to French kings too. So French nationalism obviously wasn't the deciding factor there. Also, when English rule was more or less competent under Bedford, ordinary Frenchmen were reasonably willing to fight for the English as long as they were paid regularly and treated well -- see, for example, the first siege of Paris, where the Parisians fought hard and successfully against Charles.

Finally, you can question whether any late medieval state was really set up to rule over two large, populous kingdoms. Remember, Henry V's vision was not to be a Charles V Habsburg, one man holding various crowns. He wanted a united kingdom of England and France, with England firmly on top. English nobles were given French lands and titles. The rudimentary French administrative bureaucracy was heavily anglicized. Paris was still the capital of France, but all the important decisions were to be made in London. It was a bit like the Union of Aragon and Castile a few years later in Spain, or the one between England and Scotland after 1603 -- two crowns, but definitely not an equal partnership.

Castile and Aragon were able to unite to make Spain, and England and Scotland were able to unite to make Great Britain. But you can reasonably ask whether something like this could have worked when the partner nations were as large, geographically separated, and culturally distinct as 15th century England and France.

In sum, my answer would be "there were deep forces working against it -- French nationalism, the inevitable challenges of combining two large medieval kingdoms into a unitary state -- plus the English had a run of bad luck. Plus yes also, especially in the late game, the French just pulled it out and won a bunch of key battles that somehow don't get taught much in English-speaking schools."

Hope this is helpful!