Luca's father Zinedine Zidane came to manage Real Madrid, and became Luca's manager early in his career. Luca made his professional debut for Real Madrid in their last league game of the 2017–18 season: a 2–2 La Liga tie with Villarreal CF on 19 May 2018. During the 2017–18 UEFA Champions League, he was the third-choice goalkeeper, when Madrid won their third consecutive and 13th overall Champions League title.
Born in France to French-born parents of Algerian and Spanish descent, Luca is a youth international for France. He represented the France U17s in their winning campaign at the 2015 UEFA European Under-17 Championship, and the 2015 FIFA U-17 World Cup. He was capped once for the under-20s on 23 March 2018, in a 1–0 friendly loss to the United States in Spain.