The First Fleet. as its name implies, was the first fleet formed the United Federation of Planets.
With the hostilities of the Earth-Romulan War having just concluded, the majority of the fledgling power's ships were dispatched to the Romulan Neutral Zone. When subsequent fleets were formed and assigned the First Fleet remained on its original assignment.
The USS Lionheart was assigned to the First Fleet after its commissioning.
After the Romulans joined the Federation Alliance, 40 of its ships were reassigned to Fleets fighting the Dominion.