Diane de Poitiers was actually titled Duchess of Valentinois and after Henry's death Catherine took Chenonceaux and gave Diane Chaumont.
This is Diane's chateau after Henry's death. Chateau of chaumont
And this is her other chateau of Anet (or what's left of it right now )
So I think she is pretty rich and she is really powerful according to history. She had many chateaus like that so I'd say she could have gifted Bash and Kenna one of them.