Your initial comment makes sense, as does your first reply, until you say the two force equations aren't "equal to each other". I may be losing context because the parent reply was deleted but it seems that both equations can totally be equated, which actually leads to gravitational acceleration:
F = m a = G m1 m2 / r²
Since m is either of the two masses in the second equation, we get:
a = G m2 / r²
For example on the surface of Earth, m2 = 6e24 kg and r = 6371 km which gives you:
a = (6.674e-11 m3 kg-1 s-2) (6e24 kg) / (6371000m)2
a = 9.866 m/s²+(6e24+kg)+%2F+(6371000m)%5E2) which is the gravitational acceleration on Earth (a bit off due to rounding approximations I guess).
Whether you look at it as a fictious force or not doesn't really matter. It's either your acceleration compared to the ground when you're freefalling close to the surface, or it's your acceleration compared to an inertial reference frame when you stand on the ground.