Oh yeah, that's called the melee, and is a big fight on foot between people, sometimes in teams.

There is a trope in some films/shows though, where two people are jousting each other. One gets dehorsed by the other, and out of anger, pulls the other off of their horse. The two then begin to fight each other on foot, while still in their jousting armour. This trope was most recently in House of the Dragon.