This old answer of mine outlines how medieval battles possiboy took place, although it's worth noting that we lack sufficient evidence to be sure.

In short, movie battles where two armies merge into one big mass with no distinct lines and thousands of individual combats is stupid and would result in incredibly high casualties. Instead, armies definitely stayed in distinct lines until one side or the other broke, and most likely gently prodded each other, advancing and falling back as they became fatigued or recovered their wind, until finally one side broke and ran and serious casualties were inflicted at last.