Question: 

What should be done if Eid coincides with Friday?

Answer: 

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.

 
[by Shaykh Saalih ibn Fawzaan al-Fawzaan]