I was reading about the Battle of Crècy where it was the first cited combat use and the English only lost 100-300 while the French lost roughly 2,000, then the French ended up winning the war.
If you are wondering about the 100 years war and the part the longbow played in it, I believe I can help you there. In the battle of Crecy, the English victory was due in part to the cunning leadership of King Edward III. His use of longbowmen was legendary, and the first major victory for longbows over crossbows. Their astounding success was due to the tenacity of the English archers, and their ability to keep their bowstrings dry. The crossbowmen could not remove their heavy strings. So, on the rain drenched field of Crecy, their crossbows were proven useless. So, their knights marched on without any cover. This allowed the English knights to move around with impunity, and strike wherever they felt necessary. That, combined with the ranged assistance of the English bowmen, won them Crecy. Apparently, it took them a century to fix their poor tactics, as they suffered yet another crushing defeat on the battlefields of Agincourt, under very similar circumstances. However, the crossbowmen were able to adapt, thus giving their army much needed consistent ranged support. That, and keep in mind that the French were able to draw troops from local conscription; the English were not. It would take amphibious landings to receive additional troops. Also, as armour became more and more advanced, they were able to withstand longbows more well. This is where the crossbow became the ultimate knight-killing machine. A crossbow has much more power in each shot than a bow. It was able to puncture armour more effectively, thus rendering English knights more vulnerable. However, both sides used the crossbow, and the longbow, respectively. The French just used the crossbow more, and were able to drive the English from their land, and keep their country. I really hope this helps!
Source:http://www.britishbattles.com/100-years-war/crecy.htm http://www.britishbattles.com/100-years-war/agincourt.htm
It depends on what the French commander had access to, essentially. They used pavise crossbowmen at Constance, rushed the longbowmen with cavalry before they could prepare their defenses at Patay, did the same but with infantry at Pontvallain, used artillery for psychological warfare purposes at Formigny, and forced the English to attack at Castillon (which is sometimes called "Crecy in reverse").
Generally speaking, when provided with good logistics and experienced commanders, French armies found a variety of ways to defeat English armies and the longbowmen they used. The consistent problem facing the French was usually a problem of logistics, in that French commanders could not be certain what forces would be available to them on the battlefield. This prevented effective combined arms counters to the English combined arms forces, and even blunted the force of those counters when they could muster them - look at Crecy and the inability to supply the Genoese crossbowmen with their pavises!
After the Ordonnance reforms of the 15th century, French armies were able to ensure that they had certain elements (artillery especially) at hand when battle was joined, which in turn allowed commanders more tactical flexibility in order to beat the English at their own game.