The 18-year-old who is currently part of los Blancos' youth team, was born in France but became a Spanish citizen in 2006 and represented the nation at U-15 level.
However, he has since opted to declare for France and was recently included in the country's U-19 squad, which is a source of pride for his father.
"I am proud that he can wear the French jersey for the first time," Zidane was quoted as saying by RMC. "He wanted it and he deserves it, it is not only because he is called Zidane, but he does beautiful things on the pitch.
"In any case, he is delighted to be picked and I am as proud as my dad was with my first selection."
Enzo Zidane, who has adopted his mother's maiden name Fernandez, will join the France U-19 squad for a training camp this week, but remains eligible to represent Spain in the future.