I searched for one for several months so I would like to share this information with others who might also be desperately searching for a proper swimming place.
In El Menzah 1 at the cite olympique there is a swimming stadium, the "piscine olympique". It is quite clean and you can swim 3 times per week, 1 hour at a time, for 40 dt per month. The swimming times open for the public are limited to: 6.30-7.30 from Tuesday to Saturday, 12. Protected content from Monday to Saturday and 13. Protected content from Monday to Saturday.
You must wear a swimming cap and a one piece swimming costume (ladies). To get the monthly card go to the men's entrance at the far right of the building and all the way downstairs. You need to take 1 photo with. The men's entrance is open on all the swimming times, the ladies entrance is not open at 6.30, so in the morning the ladies also have to enter through the men's entrance but when leaving, exit through the ladies entrance to get the card back.