Every fingering that fits a hand
a987
hard
accc
hard
x557
moderate · barre · no 5
a9cc
hard · no 5
a9cx
easy · no 5
What is true of it
Fmaj7 is F, A, C and E — 1, 3, 5 and 7 counted from F.
On an instrument that cannot reach all 4, the 5 goes first, in that order.
The easiest of the 5 fingerings below is a987: 4 fingers, held at the 7th fret.
None of them uses an open string, so this chord moves up the neck unchanged — the same shape 1 fret higher is the chord a semitone above.
1 of the 5 need a barre.
Where its notes are on the neck
The brass dots are F, the root. Everything else is a chord tone with its degree printed in it.
With a different note underneath
Fmaj7/A
2500
Fmaj7/C
5557
Fmaj7/E
x410
An inversion is the same chord with a different note lowest. The name changes to a slash name because the bass is what a listener hears as the foundation.