On the authority of Abu Hurayrah may Allah be pleased with him, “The Messenger of Allah, prayers and peace upon him, said, ‘Eid prayer and Friday prayer have fallen on the same day, today. Whoever prays ‘Eid prayer, Friday prayer is not obligatory on him. As for us, we are going to pray Friday prayer’ (Abu Dawood Classed as authentic by Sheikh Albaani)
On the authority of ‘Ataa Abi Rabaah, “Ibn Zubayr led us in ‘Eid prayer early one Friday morning. [Later that day] we went out to pray Friday prayer, but we didn’t see Ibn Zubayr!? Therefore, we prayed by ourselves; and when that happened, Ibn ‘Abbaas was in Ta’if.
So when we saw Ibn ‘Abbaas, we asked him (Ibn Abbaas) about Ibn Zubayr not praying Friday prayer with us. Ibn ‘Abbaas answered by saying, ‘What Ibn Zubayr did (not praying Friday prayer) was in accordance with Prophetic Tradition.”
If the day of Eid coincides with Friday, then whoever prays Eid with the imaam does not have to attend Jumu’ah (it is not obligatory on him); in his case it becomes Sunnah. If he does not pray Jumu’ah, he has to pray Zuhr. This is in the case of people other than the imaam. As for the imaam, he has to be present for Jumu’ah and lead those Muslims who attend the prayer. The Jumu’ah prayer should not be forsaken completely on this day.