[1][2] Birrou was born in the city of Vilanova i la Geltrú in Spain and is of Moroccan heritage.
[5][6][7] After graduating, Birrou left Oakland and Teruel and signed for USL League Two side Little Rock Rangers, where he played for two seasons.
[17][18][19] In August that year, he transferred to the Gibraltar Football League, signing for Glacis United where he made 8 appearances and kept 2 clean sheets.
[20] In 2024, Birrou left Glacis United to join Filipino club Kaya–Iloilo, who were defending champions of the Philippines Football League.
[21] [22][23] He made his first appearance and got his first clean sheet for the club in the opening match against United City.