As it was fought for longer than a hundred years, it's no surprise that the strategy and tactics used by all sides in the Hundred Years War evolved over time, creating two very different eras. What we see is an early English tactic proving successful, before technology and warfare changed to a French one becoming dominant. In addition, the aims of the English may have stayed focused on the French throne, but the strategy to achieve this was starkly different under two great monarchs.
Early English Strategy: Slaughter
When Edward III led his first raids into France, he was not aiming to take and hold a series of strongpoints and regions. Instead the English led raid after raid called a 'chevauchée'. These were missions of pure murder, designed to devastate a region by killing crops, animals, people and destroying buildings, windmills and other structures. Churches and people were plundered then put to the sword and fire. Huge numbers died as a result, and wide areas became depopulated. The aim was to cause such damage that the French wouldn't have as many resources, and would be forced to negotiate or give battle to stop things. The English did take important sites in Edward's era, such as Calais, and small lords fought a constant battle against rivals for land, but the strategy of Edward III and leading nobles was dominated by chevauchées.
Early French Strategy
King Philip VI of France first decided to refuse giving a pitched battle, and allow Edward and his followers to roam, and this caused Edward's first 'chevauchée's to cause great damage, but to drain the English coffers and be declared failures. However, the pressure the English were exerting led to Philip changing strategy to engage Edward and crush him, a strategy his son John followed, and this led to the battles of Crécy and Poitiers were larger French forces were destroyed, John even being captured. When Charles V went back to avoiding battles - a situation his now decimated aristocracy agreed with - Edward went back to wasting money on increasingly unpopular campaigns which led to no titanic victory. Indeed, the Great Chevauchée of 1373 marked an end to large scale raiding for morale.
Later English and French Strategy: Conquest
When Henry V fired the Hundred Years War back into life, he took a totally different approach to Edward III: he came to conquer towns and fortresses, and slowly take France into his possession. Yes, this led to a great battle at Agincourt when the French stood and were defeated, but in general the tone of the war became siege after siege, continuous progress. The French tactics adapted to fit: they still generally avoided great battles, but had to counter siege to take the land back. Battles tended to result from contested sieges or as troops moved to or from sieges, not on long raids. As we shall see, the tactics affected the victories.
The Hundred Years War began with two large English victories stemming from tactical innovations: they tried to take defensive positions and field lines of archers and dismounted men at arms. They had longbows, which could shoot faster and farther than the French, and many more archers than armoured infantry. At Crécy the French tried their old tactics of cavalry charge after cavalry charge and were cut to pieces. They tried to adapt, such as at Poitiers when the whole French force dismounted, but the English archer proved a battle winning weapon, even to Agincourt when a new generation of Frenchman had forgotten earlier lessons.
If the English won key battles earlier in the war with archers, the strategy turned against them. As the Hundred Years War developed into a long series of sieges, so archers became less useful, and another innovation came to dominate: artillery, which could give you benefits in a siege and against packed infantry. Now it was the French who came to the fore, because they had better artillery, and they were in the tactical ascendance and matched the demands of the new strategy, and they won the war.