Madame de Lesdiguieres was a lady of the 17th century French court. (I can't find out exactly if she was part of the court under Louis XIII or XIV.)
Her cat's tomb, seen in the engraving above, bears this inscription:

Une Chatte Jolie.
Sa maitresse qui n'aima rien
L'aima jusques a la folie.
Pourquoi le dire ? On le voit bien.
(A pretty cat: Its mistress, who never loved anyone Loved it madly. Why bother to say so? Everyone can see it.)

From The Book of the Cat, by Frances Simpson (London, Paris, New York and Melbourne: Cassell and Company, Limited, 1903).

Maybe that's the same cat she holds in this portrait?

** An addendum: I am currently reading Abundance by Sena Jeter Naslund, a novel of Marie Antoinette. This also takes place in the French court, though mostly in Louis XIV's time. The amount of overly-detailed etiquette, the constant intrigues, the uses and discarding of friends and allies, suddenly made me realize the probable reason both for Madame's cold reputation and deep love of her cat. As we all know, your pets love you for who you are, no matter what. Kitty was probably the only source of such love that she had. What must that kind of life be like? Isn't that sad?