Zidane came through CD Canillas before spending more than a decade in Real Madrid's academy system, and joined Real Betis in 2024 to continue his development in Spain.
He made 17 appearances for Betis's second team last season before his move to Paris was finalised.
The defender arrives at Red Star having built his career within some of European football's most respected academy structures, and the Paris club believe he can add genuine quality to their backline.
Red Star finished fourth in Ligue 2 last season and are considered a promotion candidate, making the timing of Zidane's arrival significant for a club with ambitions of moving up the French football pyramid.
A French youth international, Zidane already boasts an impressive résumé at underage level, having won the European U17 Championship in 2022 and reached the U19 European Championship final in 2024.
The left-footed defender also featured for France at last year's U20 World Cup, starting every match as Les Bleus finished fourth in the competition.
Standing at 1.96 metres, Zidane arrives in Saint-Ouen with the profile of a modern, athletic central defender and represents one of the more eye-catching arrivals of the summer given his family name.
His father Zinedine remains one of the most iconic figures in the sport, having won the World Cup with France in 1998 and the European Championship in 2000, before lifting the Champions League as a player with Real Madrid in 2002.
Elyaz becomes the latest of Zinedine's sons to pursue a professional career, following his brother Luca, who recently played in goal for Algeria at the World Cup.
Zidane departs Real Betis after two and a half years on the club's books, ending a spell that began when he arrived to complete his development away from Spain's traditional powerhouses.
His exit forms part of a wider departure of young talent from the Seville club this summer, with several other academy prospects also leaving as Betis reshape their squad under head coach Manuel Pellegrini.
Terms of the transfer, including any financial details, have not been made public by either club.
Red Star will be hoping the young centre-back's move to Saint-Ouen marks the beginning of a breakthrough season, both for the player individually and for the club's push towards the top of Ligue 2.