Hi Z-

You are right about the Cmaj7 and Fmaj7, in their "standard" configuration, as played on the guitar, They would use the C, and the F, for their bass notes.

But when you get into inversions, anything is possible. You may indeed play a version of a C chord that is stacked differently, and has a different note as the bass note. You could end up with, as you suggest, a C chord that has a G as it's lowest note.

You may see that indicated on songsheets as C/G. This is called "C over G", and it means that you are to play a C chord, but that the bass note (lowest note) you play should be a G.

Make sense?

-Lisa