used that same fingering and move the pattern up 2 frets and BARRE you have6 string = G (3rd fret) 5 string = C (3rd fret) 4 string = G (5th fret)3 string = B (4th fret)2 string = D (3rd fret)1 string = G (3rd fret)by your logic, moving up a whole step from F (2 frets) the [barre] chord SHOULD BE a G a G chord is G, B, D the C is a perfect 4th to G so if you wanted to add a 'C' to a G, you n