I'm aware that the pike was the standard weapon of footmen during this time, but I've also heard that short-swords/long knives were common during this period. Additionally, I've also read that falchions were fairly common weapons, but I have no real way to confirm this.
There was a fair amount of technological and tactical change during the period you're asking about, and "peasant conscript" is a pretty broad category.
That being said, at least in north Western Europe lower income soldiers were often equipped with a crude, machete-like long knife, sometimes called a falchion.
In the battle of agincourt, the English forces the English had about 1500 men at arms (heavily armored men who could fight on foot or on horse, think knights without the land) and 7000 longbowmen. The longbow men weren't conscripts (they volunteered hoping to get rich off loot) but they were mainly from poor/lower middle class backgrounds. The longbow men usually were equipped w a long bow, a spear/sharpened stick (that could be carried or stuck in the ground to form a makeshift barrier) and often some sort of long knife.
In an era were soldiers nearly always equipped themselves, there was often a lot of variability in weapons carried.