If ‘Eid prayer and Friday prayer (salaatul-Jumu’ah) fall on the same day, what are the options?
Answer: Dr. Muhammad Baazmool, may Allah protect him, says,
“If Friday prayer and ‘Eid prayer fall on the same day, whoever prays ‘Eid prayer, Friday prayer is not obligatory on him. Rather, [he can] pray the afternoon prayer (salaatu ath-thur)  in its (Friday prayer’s) place (Baazmool 121, 122).” 
 – On the authority of Abu Hurayrah [d. AH 57 or 58] , 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’(Al-Albaanee 179).” 
 – On the authority of ‘Ataa Abi Rabaah [d. AH 114] ,
“Ibn Zubayr [d.AH 73]  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 [d. AH 68] , 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 (the Sunnah).”
[*] – As-Shaykh Saalih Fawzaan said,
“If ‘Eid prayer falls on the same day as Friday prayer, whoever prays ‘Eid prayer, it is not obligatory for him to pray Friday prayer. Rather Friday prayer becomes recommended (sunnah) for him. However, as it relates to the Imam [of the community], it is obligatory for him to pray both ‘Eid prayer and Friday prayer. He can not leave off Friday prayer because those who choose to pray Friday prayer need an Imam. (Fawzaan 2/257).” 
Important Note: All biographies were taken from (Aadam, Muhammad). 
May Allah, the Most High, reward all of the Muslims who are sacrificing their wealth and effort to perform al-Hajj, Aameen!
Translated and Compiled by:
Jameel Finch al-Makki
University of Umm al-Quraa
Makkah, Kingdom of Saudi Arabia
Thu al-Hijjah 9, 1430 / November 25, 2009
1 [TN]: The afternoon prayer (salaatu ath-thur) should be prayed as four units (raka’aat).
2 Baazmool, Muhammad. The Object of Desire for the One Who Wants to Perform Voluntary Prayers. Riyaadh: Dar al-Hijrah. 1423/2002
3 Abdur-Rahman bin Sakhr [d. AH 57 or 58], the Companion who narrated 5374 Prophetic Traditions (Hadeeth).
4 Authentic: Al-Albaani, Naasir ad-Deen. Abu Dawood’s Collection of Prophetic Narrations. Riyaadh: Maktabah al-M’aarif. First Print.
5 ‘Ataa Abi Rabaah al-Makki [d. AH 114] was a follower of the Companions of the Messenger of Allah (Taabi’i). He was trustworthy and had a very sound understanding of the religion of Islam.
6 ‘Abdullah Ibn Zubayr al-Qurashi [d. AH 73] was a Companion of the Messenger of Allah. He was the first child born from the Muslims after their resettlement from Makkah to al-Madinah. May Allah be pleased with him. (*) I had trouble identifying this Companion. May Allah reward brother Moosaa Richardson for helping me over the phone.
7 Abdullah Ibn ‘Abbaas al-Haashimi [d. AH 68] was the cousin of the Messenger of Allah. He was known to be extremely knowledgeable about the religion of Islam. He was given the nickname ‘The Ocean’ due to his vast knowledge. May Allah, the Most High, be pleased with him.
8 Al-Fawzaan, Saalih. Selected Religious Verdicts from Saalih al-Fawzaan. Lebanon: Ar-Resaalah Publishers. 1425/2004
9 Aadam, Muhammad. A Summarized Version of the Narrators of al-Bukhaari and Muslim. Ad-Dammam: Dar ibn al-Jawzi. 1430/2009
Article Source : http://www.salafitalk.net/st/uploads/Friday.pdf
- When Eid coincides with Friday
Fatwa from Permanent Committee and Shaik Ibn Baz (rahimahullaah)