Sorry for my English, it's not native
"Don't get me wrong. I have never been in a crossbow or a longbow fight, but the Battle of Crecy was won by longbowmen zinging the French Knights to death, right?"
That's a nice legend, but reality can be quite far from our understanding of what really happened there. There were numerious scintific reconstructions - scientists found examples of iron, which was used in french armors, and arroheads of arrows of longbowmens. And, having estimated arrow speed (using special cameras, and devices) , sent by professional archer, they made experiment - English arrows with iron quality which was used during this fight against french armor of that time. And arrows when were hitting armor in most of cases didn't pierce it.
Of course, if there are a lot of arrows, and french knights were not covered ideally with it, and there we different armors, probably.. but they came to different theory which, by their belief explains what happened there.
The main difference between English forces and French was in a very high amount of long bowmen (which were just twice cheaper than footmen). These guys were not really protected a lot, were in cloth boots, some shirts...something very far from heavy armored french men. Of course there were footmen also, but proportions.
The field was chosen by English strategists, basing on this difference.
It was a very nerrow field, where French just could not attack from many siddes, and had to send all army through quite narrow place. It was rain, a lot of mud. A lot of French knights, trying to get through narrow part of the field, and shower of English arrows, which added to this mess. French, heavy armored knights, just struck in mood by their heavy iron boots.When you are in a mess of bodies and mood, you are heavy, and your heavy boots struck in a land, swampy from rain, you are quite limited..English longbowmen, with their cloth boots and no heavy staff, were much more mobile, and just more effective, killing them, just by stabbing their long knifes into faces and weak places of armors of the French.. Then huge amount of French just gave up. And, king of England, just executed them all because he didn't believe that he has already won and expected more French to come and to free his numerious prisoners.
I don't remember the film, where all this research was explained. Some made in UK, for sure.
So, long bows have quite cool reputation, but, really , it is based more on this battle, and in this battle it was strategy and weather, who brought victory to England, and long bows were maybe third factor,or 4th, 5th..etc.