Ruling when the Friday Prayer and the E`ed Prayer Come on the Same Day
When the E`ed occurs on a Friday, the Friday prayer remains obligatory because the E`ed prayer is a confirmed Sunna; whereas, the Friday prayer is an individual duty. Sunnah doesn`t invalidate an obligation, nor suffices for it. This is indicated by the following verse (What means): "O ye who believe! When the call is proclaimed to prayer on Friday (the Day of Assembly), hasten earnestly to the Remembrance of God, and leave off business (and traffic): That is best for you if ye but knew!" [Al-Jum`ah/9].
At the time of the Prophet (PBUH), E`ed occurred on a Friday, so he performed the E`ed prayer as well as the Friday prayer and delivered both sermons, and this is very famous in the books of Sunnah and the traditions. In addition, this is the opinion of the majority of the Muslim scholars: The Hanafites, The Malikites, The Shafites and in one narration of the Hanbalites.
He (PBUH) permitted the people from the outskirts not to attend the Friday prayer that day and instead offer the Zuhr prayer in their neighborhoods. The Prophet (PBUH) said: Two festivals (E'ed and Friday) have synchronized on this day. If anyone does not want to offer the Friday prayer, the E'ed prayer is sufficient for him. But we shall offer the Friday prayer." [Abu Dawood].
The majority of the Hanafite, Malikite and Shafite jurists said that the aforementioned Hadith applies to those who came from the outskirts of Medina in order to offer the E`ed prayer in the Prophet`s Mosque, and they aren`t obliged to offer the Friday prayer in principle, because they live in the outskirts of cities, far from populated areas. If they waited to offer the Friday prayer after having performed the E`ed prayer, they will face hardship and they will face the same hardship if they went home and returned to offer the Friday prayer, and this is why the Prophet(PBUH) permitted them not to attend the Friday prayer.
Therefore, it is more prudent to observe both prayers on that day, and as regards the opinion of some Hanbalite jurists states that whoever prays the E`ed prayer isn`t obliged to pray the Friday prayer, and should pray the Zuhr prayer instead, it contradicts prudence and acquittal.
As regards the opinion which states that praying the E`ed prayer invalidates the Zuhr prayer, this has never been stated by any of the four schools of jurisprudence and contradicts the provisions of Sharia which make offering five prayers for each day and night obligatory. Therefore, it is impermissible to apply this opinion, imitate it, or issue rulings based on it. Moreover, some narrations, related to some companions, state that the E`ed prayer makes the Friday prayer not obligatory if they happened on the same day, aren`t to be taken into consideration.
Finally, there is no room for dispute and argument since Muslims are about to receive the Feast of Al-Fitr, rather, a Muslim should adhere to matters whose meanings are established, leave matters whose meanings are allegorical and follow the established opinions of the four juristic schools. And Allah Knows Best.