Are braces available in the hospitals or dispensaries of Mauritius? Is it free ?

No they do not use braces as the line of treatment in hospitals or health centres in Orthdontic treatment.. Even if they did it, ethically speaking it wouldn't be free..
I agree health sector is free of charge in Mauritius but then just think a bit deeper if it were possible

As far as I'm aware, hospitals will only treat when you have a toothache or some other form of problem preventing you from eating (chewing) or affecting your health.

You may have to go to a private dentist for fillings and braces or other cosmetic surgeries.