If you are basing your harmony off of F minor, this chord progression makes a lot of sense especially wanting to use C major instead of C minor. This is very rooted in the traditional study of harmony by weaving though the 3 minor scales which are F natural minor, F harmonic minor, and F melodic minor which gives the following sets of notes:
F natrual minor - F G A♭ B♭ C D♭ E♭ F
F harmonic minor - F G A♭ B♭ C D♭ E F
F melodic minor (asending) - F G A♭ B♭ C D E F
This is a very common scenario when dealing with minor keys and is very traditional in nature. I suggest reading up more on the different types of minor scales to get a better grasp on how they are used:
As a closing note, not everything needs to be contain in one scale and you'll find a lot of the more colorful progressions venture pretty far outside of just one set of scales that defines them.