The 18-year-old, playing in Real Madrid's youth ranks and selected for France under 19s after choosing Les Blues ahead of Spain who he is also eligible for, is already being likened to his 1998 World Cup winning dad.
"Leave him alone, this is all he needs," Deschamps, who played alongside Zidane for France and Juventus, told reporters on Thursdsay at a news conference.
"His name is hard to carry. He's just a player, with a well-known name. It's never easy, and it's even less easy with his name. He won't live his father's history and I think Zizou (Zidane) will agree with me.
"Zizou lived his life, had his career. Enzo will have his own."
Zinedine Zidane, voted in 2004 as Europe's best player in the past 50 years, is now Carlo Ancelotti's assistant coach at Real Madrid.
(Reporting by Gregory Blachier; Editing by Martyn Herman)
