The History Channel had an interesting show that used a computer program for analyzing crowd flows at stadiums and shopping centers look at this battle. They concluded that many of the French would have been killed by trampling after falling in the mud. They thought the poor visibility in the suits of armor contributed to the French problems. It was interesting to see how the topography contributed so much to the French catastrophe.
Interesting...they reference this point in the article. The French were not dressed properly for the conditions...sorta like wearing cleats on frozen turf for a football game.
The guy who got replaced was a grizzled veteran, but he wasn't a tip top nobleman, and did not have the social rank to command the huge number of high nobility in the French Army. The original battle plan was that the French bowmen, crossbowmen, and skirmishers, would attack first. They would soften the English up some, and give Henry a Hobson's choice. He could either absorb the fire of the French bows and crossbows, without replying, or he could have his longbowmen expend their very limited number of arrows on the French auxiliaries, leaving their longbows useless when the main French force attacked.
Fortunately for Henry, and the rest of the English, the new French commander simply assumed victory was his, and laid his plans not with a view to winning the battle, but to making sure Henry, and the high nobles immediately around his banner, were killed of captured by French nobles, not commoners. In the ensuing battle, the French formations, trying to win honor, not victory, merged into a single jam-packed mass of humanity, slogging through the mud straight at Henry's banner.