According to a FIFA statement, the son of France World Cup winner Zinédine Zidane will now play for the Algerian national team.
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The 27-year-old has previously played for the French national youth teams.
Luca hopes the move will allow him to participate in the 2026 World Cup.
Having originally come through the La Fabrica system at Real Madrid, Luca was a regular with France youth teams, including the U21s.