Field artillery didn’t come in until the 30 years war. What made the kinds of longbows needed to shoot through French armor obsolete was the little ice age and the collapse of the food system needed to get people big enough to pull them.
The final English defeat in the Hundred Years War was at the Battle of Castillon in 1453. They were defeated by French artillery. Admittedly, this was in an entrenched camp they attempted to storm, but the technology was the difference.
The basic English tactic throughout the war was to take up a defensible position and then slaughter the French, who were generally stupid enough to march right onto the killing field.
Had the French, for example, surrounded the English at Agincourt, which they could easily have done, and waited for hunger and thirst to do their work, the battle, to the extent it could be called one, would have been a French victory. 24 or 48 hours would have done the trick. Of course, doing so was not possible for the French, as it required a firm command and did not fit into their cultural meme of the glorious charge.
The Little Ice Age and any effects on the strength of the populace didn’t really kick in until the mid-1500s. The longbow was used extensively in the English civil Wars of the Roses, at least their early stages, and was largely responsible for the truly astonishing death rates in some of the battles.