When Eid and Jumu’ah fall on the same day, the common scholarly view is that Eid does not automatically cancel Jumu’ah for everyone ; many scholars still say Jumu’ah remains obligatory for those who are normally required to attend. At the same time, there is a recognized concession in some reports for a person who already prayed Eid to miss Jumu’ah and pray Dhuhr instead, depending on the scholarly school followed and local practice.

What people usually do

Most mosques will still hold Jumu’ah, and many Muslims attend both prayers because the two acts of worship are treated as separate obligations by the Hanafi, Maliki, and Shafi’i schools. Some scholars, especially in Hanbali- based discussions, hold that praying one of the two can be enough for those granted the concession, but this is not the universal position.

Practical ruling

[6][2] [1][6] [9][2]
Situation Common guidance
You prayed Eid and your mosque still holds Jumu’ah Attend Jumu’ah if you are normally obligated to do so.
You prayed Eid and there is a valid concession in your scholarly view You may be allowed to miss Jumu’ah and pray Dhuhr instead.
You follow a school that does not replace Jumu’ah with Eid Pray both Eid and Jumu’ah.

The safest approach

If you are unsure, the safest and most widely accepted practice is to pray both Eid and Jumu’ah when possible. That avoids disagreement and matches the position that Jumu’ah remains binding unless you are covered by a specific concession.

Bottom line

So, if Eid and Jumu’ah are on the same day: many scholars still expect Jumu’ah, while some allow a concession after Eid. In real life, the best move is to follow your local imam or the ruling of the school you normally follow.

TL;DR: Pray Eid, and usually still pray Jumu’ah too; if your community follows the concession view, you may pray Dhuhr instead of Jumu’ah after Eid.