Firstly, you do not need to stay in a key for a chord sequence to 'work'. There is only one real rule in music and that is "If it sounds good, it is good." Many composers do not think in roman numerals, or about keys and come up with great music as a result.
However, this is not to say that you shouldn't. If thinking in keys works for you, then great. Just don't let it stifle what you do. I have no idea what you listen to, so it's hard to give a reference of a song that breaks the 'rules' and is still great but I'll go with Creep by Radiohead as an easy example. The sequence actually goes from a Bmaj to Bmin. Obviously these chords are not in the same key but it still works in the context they play it in. It's all about context.
I should also add if you do want to think of this sequence in terms of keys, you could say that the song is not in fact in Cm at all. It all depends on the "implied harmony" of the piece, which is to do with everything else that is going on, including rhythm, but I would say the piece is probably either in Bb Major (making Cm a II and F7 a V), or possibly Bb's relative minor, D Minor (making Cm a VII and F7 a III).
Hope this helps.