Based on the actual King Henry II of France, Reign's incarnation of the Valois king is more antagonistic overall than he probably was in real life. As the most powerful person in France, he hopes to see his son marry Mary, Queen of Scots so that France can have an edge over the Tudors in England.
Despite being the crown prince, the Dauphin Francis isn't treated very fairly by his father the King. For most of Henry's life, it does seem like his bastard son Bash has his favor more than his legitimate heirs.
But Henry's greatest love is his desire for women. He has a romance with Mary's lady Kenna. She was pretty happy into the relationship until Henry started to go literally insane and marries her to Bash for no apparent reason. Father of the Century, I'm sure.
Then his madness gets out of hand. He murders innocent people as he starts to become paranoid. Even the Catholic Church isn't too happy with him after his antics become too much.
He even gets so terrible that he wanted to put his own son Francis in an early grave and marry Mary so he could take over England and sit upon its throne.
So Francis takes up a disguise and intentionally lands a mortal wound during a jousting match. While the Francis part was non-sense that the CW came up with, Henry II's death in real life was pretty similar to what happened here.