The various French barons probably saw more advantage in maintaining their ability to repress their own people than deeper alliance with them to defeat others. Being King of France sounds nifty, but there wasn't actually much that King could do against the more powerful or remote barons. One of those barons might have had more power over the others by training archers, but the real power would be with the _archers_, and the baron would access that power by their acknowledgement of his authority. This makes it difficult for the baron to tax the bejesus out of the serfs and take their daughters. All of which was the really fun part of being a baron, and never mind about being King.

When your political status depends on your ability to beat the crap out the people around you, and that ability depends on you having expensive armor that they don't have, you have no interest in teaching them to kill you at 150 yards with a piece of wood.