Given scene/plot descriptions from movies or TV shows, and given a specific question about the scene, summarize the question into a title

In the iconic Battle of Stirling Bridge scene in the film Braveheart, English heavy cavalry knights charge with a lance in their right hand and a shield in their left hand. I recently watch this battle scene again and noticed one particular thing: English knights should have carried close quarter melee weapons. I understand for heavy cavalry, they are supposed to charge towards their enemy over and over again on their horses, but should they not consider taking a melee weapon with them, for example, a mace, a sword or a dagger so that they can defend themselves when they become dismounted. I think it is a detail Mel Gibson overlooked when making this movie.
Are the cavalry knights missing close melee weapons in Braveheart?