Sorry, I just seen this. It did not appear on my alerts. Originally perez wanted him to be a director of football, but zidane wanted a more "hands on approach" and to work with the players more. His main duties include tactical preparation and he also deals one-on-one with players who need help or support. Here are quotes from an interview he did a while back. I hope this can give you the answers you want and more of an insight into his role.
“I analyse the goals we concede, how it happens, in what minute, and help to prepare for games,” Madrid’s assistant coach said. “Paul Clement prepares the training sessions and I work more on tactics and with the players alongside Carlo. I am always available for the players. When someone is not feeling good, I am here to talk if he wants, if he needs me. Whatever the player asks.”
“With Ancelotti things have been done in a natural way,” Zidane said. “It was a good moment for me, for the club, and for Carlo. I could not have taken this position with a coach I did not know. I could not have been Mourinho’s assistant, for example, and anyway he already had his second in command. There was no reason to do it with him.”
“I am on the normal path to being a [head] coach,” Zidane said. “I am learning a lot with Carlo. I know what I want and I am capable of achieving it. I want what I am doing now to be useful for me in the future. I want to build something, and within 10 years we will do another interview and the balance of what I have done will be positive.”