If the day of ‘Id occurs on Jumu’ah, then salatul Jumu’ah is no longer an obligation upon those who performed the salatul ‘Id.
Zaid ibn Arqam says: “The Prophet sallallahu alehi wasallam prayed the salatul ‘id and then he gave an exemption concerning the Jumu’ah, saying: ‘Whoever wishes to pray it may pray it.'” This is related by the five and al-Hakim. Ibn Khuzaimah calls it sahih.
Abu Hurairah reports that the prophet sallallahu alehi wasallam said: “Two festivals have occurred together on this day of yours. For whosoever desires, this will suffice for his salatul Jumu’ah, but we are going to perform salatul Jumu’ah.” This is related by Abu Dawud.
It is preferred for the imam to perform the Jumu’ah so anyone who wishes to perform it may do so as well as those who were not able to attend the ‘id prayer. The Prophet sallallahu alehi wasallam said: “We are going to perform the salatul Jumu’ah.”
According to the Hanbali school, the zuhr is obligatory upon anyone who does not attend the salatul Jumu’ah because he has performed the ‘id prayer. Nevertheless, it apparently is not obligatory as there is a hadith in Sunan Abu Dawud in which Ibn az-Zubair says: “‘Id and Jumu’ah occurred on the same day so he joined them and prayed two rak’at at an early time, and did not add anything to it until ‘asr.