In many ways, they did. The English simply adapted their tactics aswell, and when the French managed to develop their systems of administration and military organisation, aswell as their use of early gunpowder weapons, then they managed to push the English back.

The primary strategy of the French military elite, going into the war, was the furor franciscus, the concept of hitting the enemy with such force and such ferocity that they recoiled. This is very beautifully laid out in the opening chapters of The Road to Crecy*, by Marilyn Livingstone and Morgen Witzel. While relying upon the mounted component at Crecy, it is unfair to say that it was the tactics that led exclusively to the French defeat there.

The Duke d'Alencon, King Phillippe's brother, rushed into battle prematurely, and the order to stop and regroup after the march was either not properly transmitted or simply disobeyed. The French Army arrived piecemeal, and were subsequently defeated in turn by the English. In this sense, many of the warriors who fought at Poitiers attributed the defeat at Crecy to the treachery of certain nobility and the arrogance of some grand seigneurs.

They did, however, remember the horrendous damage done to horseflesh at Crecy, and in the south around Aguillon. That campaign is in itself a fantastic example for any medieval historian, as the Earl of Lancaster was really, really FUCKING good at fighting (look Kenneth Fowler's The King's Lieutenant, damn good read). Anyway, the French at Poitiers and Agincourt fought primarily on foot, and understood that the archers needed to be eliminated. Attacks were made by cavalry charges and an infantry attack at Poitiers to try and quickly sweep the English archers from the field/. Both failed, but this is clear evidence of the French updating their tactical doctrine to try and counter the immense killing power of the longbow.

It must be mentioned that while Agincourt was a horrendously bloody battle almost from the outset, Poitiers was a damn near thing. Had the Duke of Orleans committed his troops, had the Prince of Wales not utilised some of his Gascon troops to strike at the rear of the troops.

In brief, the French did, indeed, utilise counter-measures to the English longbow. Better armour was produced and worn, cavalry was reserved for trying to flush out the longbowmen as quickly as possible rather than against the main battleline, and there were plenty of occasions where the longbows were defeated.

But the English at Agincourt, Crecy and Poitiers were well-led, well-trained and well-organised. They used the ability of the longbowmen to hem the French in, and adapted this strategy to great effect whenever their enemies came up with a counter-measure. At Crecy, the arrows were used to rip through the French horseflesh and thereby leave their riders vulnerable to attack and further missile fire (Jonathan Sumption, Trial by Battle). At Poitiers, they were used to force the French to make rash decisions and hem them into a killing ground (David Green, The Battle of Poitiers). At Agincourt, they further fatigued the enemy, neutralised the cavalry, and then fell upon the flanks of the primary French formations (Juliet Barker's Agincourt: The King, the Campaign, the Battle, do not believe Anne Curry's lies).

It wasn't that the French didn't adapt, it was just that the English adapted aswell. One must not forget who won the Hundred Years War, and I'm sure Orleans, Castillon and Patay ring just as true in any Frenchman's ears as Crecy, Agincourt and Poitiers.