Besbes was born in a sports family: her father Ali is a former basketball player, who became a physical education teacher; her mother Hayet Ben Ghazi is a former foil fencer, who became an international referee. Her parents settled in Abu Dhabi before she was born. They had all their children–daughters Azza, Sarra, Héla and Rym, son Ahmed Aziz–take up fencing. Sarra competed in the women's épée at the 2012 Summer Olympics in London, while Héla is also a sabreur, member of the Tunisian national team.