Tournament Joust is a free print and play game with some really good looking jousting mechanics. It has paper knights, but you’ll want to swap in your own miniatures.
Rules: Medieval
Legends of the Feudal Times Skirmish Rules
Games Workshop’s Lord of the Rings rules set has turned out to be very flexible, spawning several commercial sets, such as Legends of the Old West and Legends of the High Seas and innumerable fan variants. Legends of the Feudal Times is a set of feudal skirmish rules originally published in the French language magazine Vae Victis. The English translation is here.
A Great Victory Pregunpowder Era Rules
A Great Victory is a set of free wargames rules for miniature wargames set in the pregunpowder era.
God Will Know His Own: Rules For Knight and Crossbow era 1096-1590 (or 1789)
God Will Know His Own is a set of free wargames rules for “Knight and Crossbow era Wargame Rules 1096-1590(or 1789) then into the horse and Musket era.”
Wars of the Roses Supplement for LoTR Strategy Battle Game
Here’s a Wars of the Roses supplement for the Lord of the Rings Strategy Battle Game. The original link has died. I’ve attached a copy below.