There's quite a bit of mythology and misinterpretation passed around about Crecy because of its fame and prominence. First of all, there's debate about the identity of the French missile troops present at the battle. While they are typically described as "Genoese" by our primary sources, payroll records tell us that the number of professional mercenary crossbowmen from Genoa would most likely be less than the figure of six thousand that is most commonly cited. Were the numbers exaggerated (which would be typical of medieval sources), or were these "Genoese" crossbows actually a mixture of French militia troops and true professionals? There's been debate on the subject, but as far as I'm aware, no true consensus. Personally, I find it doubtful that the French fielded anywhere close to six thousand crossbowmen of any origin. Two or three thousand is a much more likely number.

With the question of numbers and origins addressed, we can look at some other factors contributing to the defeat of the French at Crecy. Gallons of ink have been spilled in quibbles over the technical capacity of the longbow vs the crossbow: poundage, range, rate of fire, etc. The typical narrative also tells us that the wet bowstrings of the French crossbows also had an effect. Personally, I am less convinced that the wet strings mattered very much given two other factors: 1) the English had around 5000 archers (estimates range from 4-7 thousand), which would have given them a numerical advantage over the French bows, and 2) the French crossbows lacked their shields. This wasn't because they forgot to bring them, but because the pavises were stuck in the baggage train, which wasn't in a position to do much of anything. The French army as a whole was hampered by the congested terrain of Crecy. The English had deliberately chosen a place to fight where they were able to defend themselves without being easily outflanked or charged. The French army lacked the room to properly arrange themselves for battle. Since the combat troops had difficulty getting into position, the situation would have been even worse for the baggage train, which would be placed at the rear of the army for its own protection. The resulting lack of pavises was a fortunate coincidence for the English.

As for the infamous trampling of the crossbows, I lean towards the side of the debate that argues that the skirmishers were ridden down by accident rather than a deliberate order. I'm sure some of the frustrated French knights did so with a certain amount of enthusiasm, but on a battlefield as crowded as Crecy, it's not surprising that the advance of the cavalry would result in friendly fire. There simply wasn't room for the crossbows to go anywhere without disrupting the other troops on the field, which created a dangerous situation when the other soldiers begin trying to go the opposite way. Professional crossbowmen were an expensive and valuable asset and, contrary to common belief, knights did not believe that bowmen were useless peasant scum.