Non-Canonical
In the novel Articles of the Federation by Keith R. A. DeCandido, the Federation Council is depicted as being housed in a 15-story building in Paris called the Palais de la Concorde. The Council chambers are located on the first floor, while the presidential office is located on the top floor; the Council itself determines who may run for the office of the presidency, and is divided into a number of "sub councils," to which the president appoints members with the full Council's approval. The Security Council, for instance, deals with matters of Federation security, while the Judiciary Council can make rulings on judiciary matters (that seem to overrule those of the Federation Supreme Court. As of 2379, the President of the Federation is Nan Bacco, a human woman who hails from Cestus III.
Read more about this topic: Federation Council (Star Trek)