My husband lived and worked in La Goulette , too. But he only knews a house without furnitures. Or a nice hotel,at the beach, but I think this might be too expensive.
He said it´s not a good period to look for an appartment, because all the tunesian people are looking for one to spend their holidays.
But if you search and ask some people there you may find, but its not easy.
La Goulette has a nice beach, and its nice to stay there also for your wife and children, I stayed there also 3 weeks.