Golf: there are two 18-hole golf courses nearby, at Béziers and Carcassonne, and a third slightly further away, south of Perpignan. If you're feeling a bit less energetic, there are numerous mini-golf and crazy golf courses in the area too...
Swimming, ice skating and ten-pin bowling: all available at the Espace de LIberté in Narbonne, that also offers a buffet-style restaurant.
Rugby: Narbonne is home to the rugby union team Racing Club de Narbonne Méditerannée (RCNM), that was founded in 1907. They play in orange and black at Narbonne's Parc des Sports et de l'Amitié.