Well let's look at the various eras:
ENT - If a capital ship has such a low number of weapons then it would be impossible to create a fighter with at least one cannon.
TOS - still no weapons for small vessels and I won't even speak about the low warp speeds
TNG - finally something akin to fighters is shown, I cannot consider the Maquis or the Federation attack crafts as fighters, and the Runabouts are a step in the right direction. But we have a true fighter in Insurrection (the Ventrue/Talon-class).
In regard to fighters, you better take a look at Invasion and Shattered Universe, as both these games depicted the fighter in 24th and 23th centuries respectively.
So it seems like the Federation had fighters since the end of the 23rd century.