Tounkara was part of several French youth teams. She debuted for the France U16 team against Norway on 4 July 2011. Tounkara also represented France in many international competitions. In 2012, she was part of the squad that played at the UEFA Women's Under-17 Championship, in which France finished second. In September of the same year, she was called to represent France at the 2012 FIFA U-17 Women's World Cup in Azerbaijan. Tounkara was a titular along the whole tournament and played the final match in which France defeated North Korea on penalties and became champions. In August 2013, Tounkara traveled to Wales to represent France U19 at the 2013 UEFA Women's Under-19 Championship. The team did very well, defeating England in the great final and taking the title. In August 2014, Tounkara was called to represent France U20 at the 2014 FIFA U-20 Women's World Cup in Canada. The French team finished third. In 2017, she was part of the squad that represented France at the UEFA Women's Euro 2017.