Genestet was a member of the French U–21 side from 2010 through to 2013. In 2013, he was a member of the team at the FIH Junior World Cup in New Delhi. At the tournament, the team made history by securing France's first medal at the event, takinghome silver.
Genestet also debuted for the France national team in 2010, and has been a member of the team since. He represented France at the 2018 World Cup. He is the current captain of the national team.