The French get a bad rap in a lot of older scholarship and, as a result, also in pop-history and movies. The near-constant defeat of the French has been taken as evidence that the French, in their arrogance, preferred to keep their "chivalric" tactics and rely solely on the massed cavalry charge and individual prowess for most of the the Hundred Years' War. This is likely where the writer and director of The King were coming from when they portrayed the French attacking all mounted in two suicidal charges.
The truth, though, is that the French already made massive changes in how they fought by the time of Agincourt and, importantly, they made many of these changes early in the HYW, not late. While they had never relied solely on the cavalry charge, having made extensive use of combined arms tactics all the way back into the 11th and 12th centuries, they altered this dynamic considerably during the first decade of actual combat against the English.
I'm going to trace the development of French tactics through the end of the 1360s, where they had very nearly completely matured their tactics against the English. Some minor alterations were made before Agincourt, but for the most part the tactics at Agincourt were no different from those at Restellou or Mauron.
French Tactics Prior to the Hundred Years' War
Starting at the Battle of Courtrai in 1302, we see the French combined arms system as it had been more or less for several centuries. Both the French and the Flemish put their crossbowmen out in front of their lines, with the French placing light infantry (bidauts, Spanish javelin men) behind their crossbowmen to bolster their line. Behind the Flemish crossbowmen, though, was a solid formation of infantry, while behind the French crossbowmen were mounted men-at-arms. The French crossbowmen drove off their Flemish rivals, and the Flemish line moved back from the edge of the stream in order to get away from the French missile fire. The French crossbowmen, however, were running low on bolts and the bidauts were not adequate for standing up to heavy infantry, even if they were good at skirmishing. If either force crossed, the Flemish would probably destroy them against the stream.
On the other hand, the Flemish did look to the French like they were in retreat and, if pushed immediately and not given time to regroup, could be defeated. They therefore launched a cavalry charge across the stream. This is where they went wrong - there wasn't enough room on the other bank to fully regroup after crossing, and there were a number of ditches on the other side that were full of water and broke up the French formation further. The result was that the French didn't have the space to launch their charge, except in the center. There they very nearly broke through, and some of the men there began to flee, but reserves came up and reinforced it. As a result, the French were forced back against the stream and into the ditches all across the battlefield, which is where most of the casualties were taken.
It really needs to be understood here that the French were very nearly successful. True, they did underestimate their opponents and also misinterpreted a tactical withdrawal for the beginnings of a rout but, in spite of the sup-optimal battlefield conditions, they came close. Had the battle been fought on open ground, they still might have lost, but the battle wouldn't have been the disaster that it was.
By the time of the next major battle, Mons-en-Pévèle in 1304, the French altered their plan of attack slightly. They brought along siege engines to target the Flemish formation - although the Flemish managed to destroy these before the battle started - and started off by skirmishing and staging a false charge to test the Flemish resolve. When this failed, they tried repeated charges in conjunction with an attack on the wagenburg at the rear, but this failed as well. After retreating to their camp, Flemish went on the offensive and attacked the camp. This plan almost succeeded, but failed when the French rallied and attacked the disordered Flemish infantry, solidly defeating them.
Cassel, in 1328, was the culmination of what the French had learned from Courtrai and Mons-en-Pévèle. The French again deployed some siege engines against the Flemish, but rather than mount cavalry charges they stuck to skirmishing and ravaging the Flemish countryside around the static Flemish position. In essence, they besieged the Flemish camp and forced them to take the offensive. When they did, a mounted reserve was used slam into their flank and crush them. The heavy losses suffered in this phase of the battle meant that the French could then break the final Flemish defensive formation and claim total victory.