Translation:The President of France does not agree with me.
The French President does not agree with me ----Not accepted! Cén fáth?
I would guess it's analogous with the difference between the Republic of Ireland and the Irish Republic in the context of Poblacht na hÉireann
Because that's not what the sentence says?
(A French person could be the President of any institution; in the sentence here, the person is specifically the President of a particular country (without the nationality of the person being specified, however).