I've only read the abstract, so I'm not sure if this is covered, but the longbow requires huge amounts of practice from a young age to be effective. You had to be incredibly strong just to draw the string. A crossbow, by contrast, was easier to draw, and men could be trained to use it in a far shorter time. English Kings had constant problems with procuring enough men capable of using a longbow, passing all sorts of…
It is covered, the paper lists a number of measure the English crown took to force people to train with the longbow in their spare time.
> the French simply couldn't find enough trained men?
The French could have taken the same measures of mandating longbow ownership and strongly "encouraging" longbow training (by setting up tournaments and forbidding other types of leisure)