I think you would be interested in an older answer of mine here.

The feudal system in England was much more centralized and gave Angevin kings more direct authority than their contemporary Capetians. This allowed England to raise large forces and undertake long campaigns despite its smaller population.

The Valois kings come to accrue more authority over the course of the Hundred Years War. The later Lancastrian phase of the war is really a French civil war between the Armagnacs and the Burgundians with the English backing the latter.

After defeat of the Valois dukes of Burgundy at Nancy in 1477, the French crown became the real authority in France. In fact, many historians consider it the end of medieval era in France.

This is the first time I try to give an answer on this sub and I'm no historian, so I hope it's not going to be too bad.

u/Cracker_in_the_Rye's linked post gives a clear explanation of the political advantage that England had, being a much more centralized country. It had less ressources than France, but they were way more easily available to its Kings than France's ressources were to the Capetian Kings.

I want to emphasize the difference between the military forces of the two countries, because England had a vast advantage here as well.

The french army was, in this period, far from being a professional force. In fact it was not even an army in the modern sense. The word used to designate it at the time was the ost, which was more of an improvised assembling of heterogeneous troops than a real army. It can be divided into 5 different groups :

1. the knights, who, as vassals of the king, owed him a certain amount of time of military service. The King could thus make a call to arms to gather his vassals (and the vassals of his vassals, etc) and assemble a large corps of heavy cavalry (knights being specialized in this type of fighting). However the knights, despite all their bravery and sometimes intense training, were not professionals; most importantly, those who possessed lands (the dukes, counts, etc) were fighters but also political leaders, which could create tensions between them and the King. The duke of Brittany for example was a vassal of the King of France, but he didn't lift a finger to help his overlord until 1449, when he had been directly targeted by the English forces. Flanders, Burgundy, Foix, Béarn, Gascony of course (since it belonged to the king of England) were other examples of domains ruled by nobles who were theoretically loyal subjects of the King, but who actually pursued their own objectives and even sided with England on many occasions. Still, on the battlefield, the king could rely on those who did answer to his call to fulfill their duty as honorable knights; but even then, the king could not command them as he wished, and cohesion and discipline were generally lacking.
2. militiamen from the towns and cities. Almost all urban agglomerations were tied to the king by a chart which generally specified that if the king demanded it, they had to provide him with what soldiers they could field : archers, crossbowmen or infantrymen (never cavalry, because what urban dweller could own a horse ?), which belonged to a local defence force. Each town had a different chart with different obligations : for some, the military service was restricted to 100 men, for others to 200, for others to 300, etc (it never went beyond 500). For some, the militias were obliged to fight for only a week; for the city of Rouen for example, it was a mere day ! And other towns had charts which made their military service conditional : only if the army was led by the king himself, only if the campaign was to take place in the surrounding region, etc. Still, the king could count on these infantrymen to swell the ranks of his troops, but then again, they were not professional soldiers, simply local militiamen armed to defend their town.
3. sergeants; these were commoners who fought on horseback in most cases and served as auxiliaries to the knights.
4. conscripted peasants. This was really only an emergency measure, but it existed : it was called the arrière-ban, and it meant that the king could conscript any valid male peasant from 18 to 60 years old into the ost. They were woefully unprofessional, undisciplined and even ill-equipped, since every one in the ost had to equip himself as he could; the lords were generally asked to give weapons to these peasants, but they were often reluctant to do so, for obvious reasons.
5. mercenaries. In these category you can find the genoese crossbowmen for example. They were simply men who had expertise and equipment and lended their service to the highest bidder. This was costly, so the Kings could rarely afford to hire great numbers of mercenaries.

So with all that, the King of France could at best muster a force of 50,000 men, with as many as 28,000 cavalry men. But having vast numbers isn't necessarily an advantage, as it makes the army more difficult to manoeuver on the battlefield and to supply correctly. More importantly, this was not an army, and rather a "armed continuation of society", to quote historian Jean Kerhervé : there was very little professionalism, and most importantly no cohesion : the knights despised the commoners, the commoners despised the knights, and everyone despised the mercenaries, to put it in a slightly caricatural way. You can see the effects of having such a peculiar army at the battle of Crécy. The french battle plan was not to blindly charge the English; the french knights had learned the hard way at Courtrai (1302) that tightly packed infantry with solid defensive positions was sure to crush any frontal assault, and they had subsequently adapted their tactics, scoring important victories against the same type of troops at the battles of Mons-en-Pévèle (1304) and Cassel (1328). However, this was in theory. After a long day of exhausting forced march in the mud, the french ost was pitted against the english army by Philip VI, who refused to let it rest to keep the english army from escaping to the nearby english-friengly Flanders. The idea was to soften the english defensive positions with rains of crossbow bolts before destroying it with a cavalry charge. However, the crossbowmen were fighting without their pavises (they had had to abandon it to advance as quicly as possible), had both feets in the mud and were less numerous than the english archers. Seeing the mercenaries being routed, the knights lost their nerves and launched an all out attack on a fortified up-hill position. The issue of the battle is well know, but as you can see, it is understandable given the structural weakness of the french forces in this period.

I'm less knowledgeable about the english side, but I'll do what I can. On this side, you have a true army, and not an archaic ost; it is composed of knights, who are way more obedient to the king given the power of the king in England, but also of soldiers, i.e. men who receive a solde (a salary); several reforms undertaken in the 13th century, notably by Edward I, gave birth to a force of professional soldiers, each parish having to train a portion of its inhabitants; then, the king and his administration recruited these trained men with the endenture system and were able to muster a large force (at Bannockburn, Edward II had at least 20,000 men) composed of disciplined soldiers and knights. What's more, it could be divided at will in smaller sections, each placed under the command of a man appointed by the king for his competence. It was thanks to this system that England could rely on commanders such as Jean de Grailly, John Chandos, Robert Knolles, etc, some of them even being commoners, whereas the French King had no choice but to appoint the most powerful of his lords to assist him in commanding the army, even when said lords were inept. And lastly, I must add that the english commanders had gained invaluable experience in their ever lasting war against Scotland; in particular, the battles of Dupplin Moor (1332) and Halidon Hill (1333) had demonstrated how devastating could a well-entrenched and disciplined force using combined arms approach be, even against greater numbers.

To finish this post, I must add that the war was way less one-sided than pophistory generally puts it : England dominated the war from 1346 to 1369 and from 1415 to 1429, but the rest of the time it was more complex, and France had its own periods of domination, notably under Charles V and in the last years of the war, precisely because in this periods the kingdom abandoned the massive osts that had been defeated previously and replaced them with smaller and more professional forces. This was particulary sensible after the decisive reforms undertaken by Charles VII during the truce of Tours, which gave birth to a real army, a standing and professional one, with strictly divided sections, permanent commanders, and a massive and state-of-the-art artillery branch.

Sources :

Histoire de la France, La naissance de l'Etat moderne 1180-1492, Jean Kerhervé

The Hundred Years war, Christopher Allmand

Some things that have not been mentioned in the current responses. Some of which, bluntly, have major issues in terms of factual accuracy and depth. I am speaking much more to the Edwardian phase of the war here, but some of it applies generally:

-In many of the large set-piece battles of the war, the power of the English (often actually Welsh) longbow in the English mixed-arms formations pioneered during Edward III's reign provided a significant tactical advantage that allowed the English to overcome numerical inferiority at Poitiers, Crecy, and against the Scots at Halidon Hill and Neville's Cross. England kept winning battles against larger forces, providing them with ransom money, prestige, momentum, and capturing the Scottish king, and then the French king a decade later.

-The fighting between England and France encompassed a number of smaller internal French conflicts which often took on the characteristic of proxy wars between England and France. A succession war in the Duchy of Brittany in the first stage of the war, the Argmagnac-Burgundian conflict in the latter stage of the Hundred years war.

-English Strategy in the first stage of the conflict, wide-ranging fast-moving chevauchee from "sally ports" on the French Coast also worked to an extent against French numbers advantage, keeping forces dispersed or tied down, as did the semi-autonomous (sometimes completely uncontrolled) behavior of English-aligned routier bands who took advantage of and further contributed to the breakdown in French Royal authority, forcing France to defend and fight on a large front. This front was also sometimes not linear at all, and security broke down across wide regions of France.

-There was something of a snowball effect in the early stages of the war for the English, early victories allowed them to attract indentures and high-quality retinues under great captains, providing a high quality among the forces they did field. The french not only suffered higher casualties but increasingly French magnates and cities were unwilling to pay the high costs of defense, when the defense was ineffective and they were still being threatened by English forces and routiers, and for a while suffered a vicious cycle of declining crown revenue and declining internal security.

-Certain individual events had a paralyzing effect on French efforts, such as the capture of Jean II at Poitiers and the long periods of mental illness of the later French king Charles VI

-There is some consensus that England had both Edward III and Edward of Woodstock were gifted campaigners and battlefield commanders, although their failure to prosecute an effective overall strategy is criticized. Command also shaped French fortunes, with much greater success under certain commanders such as Bertrand de Guesclin.

-there is some evidence that the government structures and administration of England weathered the Black Death better than the French (remember 55-60% of the population died, this was a massive cataclysm for both countries).

So there are a lot of different factors, as well as the simple fact that France had much more difficulty launching a campaign into England that England did into France, particularly after the capture of Calais and other ports by Edward III.