The Federation President is the Commander-in-Chief of the Starfleet in the DS9 era
From DS9: Paradise Lost:
JARESH-INYO: Your story has a certain logic to it, gentlemen, but what
it lacks is proof.
SISKO: You want proof? Order Admiral Leyton to
withdraw his troops from the streets. See what he does.
JARESH-INYO: You think he would refuse a direct order from his Commander-in-Chief?
SISKO: If he orders his troops to stand down, then I'm wrong and I'll
offer my resignation. But I don't think that's going to happen. With
those troops in place, Admiral Leyton controls Earth. And he's not
going to give up that control until he's convinced that he has ended
the Dominion threat.
This part definitely shows that the Federation President has the authority over the admirals and can exercise it (although, due to the complicated situation in the episode, it is suggested that Leyton may decide to disobey that order).
In Star Trek VI: The Undiscovered Country the C-in-C is the highest-ranking officer in Starfleet, who, according to Memory-Alpha (I haven't found any canon sources), takes orders only from the President and the Federation Council. This may suggest that both bodies can exercise authority over Starfleet, through the C-in-C.