On this page of the Assassin's Creed Valhalla Siege of Paris guide, you will find information about the good and bad endings.
According to the game, killing Charles the Fat is treated as a bad ending. You will defeat him in the final mission, called The Madness of King Charles. He will not want to talk to you. The king will attack Eivor immediately as soon as he sees them.
After this ending, Odo takes over in France and Toka takes Siegfried's place. She will be your ally. Only Queen Richardis resents you.
However, the king can be saved. All you have to do is open the metal bars - use the lever that is on the wall. After the second stun, throw the king behind the bars and then close them. The king will be locked, but alive.
After this ending, Odo also takes over in France, and Toka takes Siegfried's place. She will be your ally. Also, Queen Richardis will be pleased with this turn of events.