If ‘Eid is on a Friday, then according to Imam Ahmad (r), the one who attends the ‘Eid prayer does not have to attend the Friday prayer if he does not wish to. This is the official position of the Madhhab.
However, attending the Friday prayer is better still, due to the strong difference of opinion on the matter. The one who does not wish to attend the Friday prayer would still have to pray Dhuhr.
[See Kashaf al-Qina’]