In these armies archers (where they existed) had been riding horses, not marching on foot and they were privileged troops and did not even always considered an “infantry” which was on a bottom of the ladder and quite often simply did not exist as a branch: it does not look like the French had an “infantry” in any of 3 famous battles of the 100YW and they did manage to outmarch the English in 2 of them.
I'm not sure where you're getting your information from, but infantry were very much a part of late medieval armies. Aside from anything else, they were necessary for fighting defensively, fighting in sieges, fighting on ground unsuitable for cavalry, and so on, and were much cheaper as well.
Armies had been lance-based (ditto for the condotierry in Italy) and more or less meaningful infantry were various city militias which were usually acting not too far from their homes. The most prominent, for a while, were Flemish militias (mostly from Ghent) and they seemingly had been as heavy as possible (mail at Courtrai and probably some plate at Rosebeke) but it does not look like prior to Rosebeke they even tried to march away from a battle under unfavorable circumstances, which can be attributed either to their speed of march or to their arrogance or both.
The prominence of city militias had ended by the start of the 14th century. After that, most infantry were either professional mercenaries or in the retinue of a king or lord. There are also examples of armies acting far from home -- the English in the Hundred Years' War, for example.
It seems that the 1st European professional infantry, Swiss, were not overburdening themselves with an armor: soldiers may or may not wear any and the same goes even for the helmets. The same goes for the landsknechts (unless we assume that most of the contemporary depictions are pure fantasy).
Switzerland was a relatively impoverished region at that time, which may have had something to do with their lack of armour. By the time other nations started copying them, muskets were becoming more important, and it wasn't practical to give mass infantry formations armour thick enough to defend against musket balls. And the Swiss weren't the first European professional infantry; as mentioned above, there were mercenary companies, and soldiers in noble retinues, long before the Swiss rise to military hegemony.