A large variety of accomodations, hotels or flats, can be found within the walls of Pau old city.

Aside typical website (e.g. booking.com), two website allow finding accomodation, plus some tourisms informations and tips : 

https://www.tourisme64.com/hebergements/pau/ (French)

https://www.france-voyage.com/tourism/pau-654.htm (En or Fr)