I have a theory. A pretty detailed one, too. Note that whenever I mention the dead girl, she is probably alive at the moment.
Rotom was the family's Pokémon. It was an ancient pokémon. Giratina created it. The family found it before Giratina had the chance to make another one, so no more were created. However, Rotom had "flaws." It was evil, but cunning. The family moved into the mansion. They consisted of a mom, dad, butler, and triplet sisters. The 3 sisters were Fantina, Gardenia, and the dead girl ghost. The girls hung out with Mr. Backlot as best friends. The family was mainly French, so it was a household language. Gardenia and the dead girl never liked the language, so they never spoke it. That is exactly why Fantina cannot decide whether to speak to you in English or French. Anyway, the Rotom loved electrical items, and the most powerful in the house was the TV. It spent all night sleeping in there. At day, it would haunt everyone, or it would imbue its Ghost powers into other objects to see the results. One day, the Rotom was about to possess one of the statues in the front of the mansion while Mr. Backlot is over at their house, and it accidentally possesses the dead girl. She goes on a killing spree, and tries to murder her sisters and Mr. Backlot, but instead, the butler gives his life for Fantina and Gardenia. Rotom takes himself out of the girl. The dead girl realizes what she has done, so she tries to start a new life. She uses TM50 on herself. It only works because a part of Rotom is still in her, but it still is useable because it was used on a human. She then knows Substitute, so she poisons her counterpart to give the illusion that she's dead. The dead substitute aimlessly wanders the house for eternity along with the butler. The real girl escapes. She is Cheryl in Eterna Forest, scared to go back to the Old Chateau. That's why Gardenia and Cheryl look somewhat alike(green hair, at least). The family abandons the mansion and the Pokémon. Gardenia raises Grass and Poison type pokémon to figure a cure for the poison of her sister, but she keeps the types after it is way too late. She concocts the Old Gateau years later and places it in the mansion to honor her "dead" sister. Fantina raises Ghost pokémon since it has a type strength against Giratina(dark types don't work because of the dragon part), and she wants to defeat it for what happened to the family. Cheryl raises Chansey bacause it is supposed to be lucky, and she doesn't want another situation like the one that happened long ago. Mr. Backlot wants to forget about his friends, but he takes the statue that was going to be possesed back to his mansion and instructs everyone not to touch it because it might release Rotom.
That pretty much explains everything sensible that deals with the Old Chateau. Any suggestions, ideas, or comments will help, and I'll edit it.