I'm not sure that the idea of knight units is historical at all. IIRC they normally served in units of men-at-arms which included knights and non-knights (usally more lightly equipt than the knights, of course.) AFAIK foot soldiers did not normally serve in units of swordsmen, with exceptions such as Scottish clansmen or Gallowglasses, so I don't think you can have historically accurate generic Catholic sword infantry whatever you call them.

The term sergeant had two meanings really, not counting sergeants-at-arms who would be part of a royal body guard. In France it meant men who provided their lord with military service in exchange for land, but did not hold the rank of knight and were not normally rich enough to afford the full equiptment of a knight. You might think of them as a light version of knights, definitely part of the men-at-arms units. This would be an accurate name for the mounted sergeant units except that they should be incorporated with the knights into men-at-arms units.

In England, the rank of sergeant did not exist as an official part of the feudal system, so sergeant became a generic term for fighting man. I suppose that means the term is justifiable for spear infantry.