The style seems to be of the sixties. The woman seems to be in her twenties or thirties. If it is not a phantasy painting perhaps they used the wrong name? One of the daughters of the then Duke François Xavier is a possibility although I do not see a striking resemblance. None of them have the name Louise somewhere in their names though. Another option is Pss Marina de Bourbon, née Gacry, who owns a perfume label with her own name.
Could it be the daughter of the brother of the current Duke of Seville?
Alejandra María Luisa de Borbón y Yordi 24 May 1976 but her age make's it more doubtful.
I doubt, as her hairstyle is more like 60ies and the painter Pierre Piget lived from 1907-1990, so again doubt this would be his final painting of a 14 year old girl. :(