Our next chord is [F] major
The first (1) and second (2) finger on the “G” and “E” string are quite traditional. So, try changing from [C] to [F] using your third finger (3) for [C] and then your fourth finger (4).
You should find that your hand “swings” more easily between the chords using your little finger for the [C].
The chord [F] can also be played by leaving the little finger (4) on the third fret of the “A” string and adding the first (1) and second (2) fingers as for the standard [F]. We’ll call this [F1]. In a twist on the old comedy sketch, “The notes are all there but not necessarily in the same order”.
Here things get really neat. Try strumming along keeping your little finger (4) in the [C] chord but adding and removing the [F] fingers (1) and (2) on alternate strums.
Beginning to sound interesting?
[C] down/up [F1] down/up [C] down/up [F1] down/up [C] down/up [F1] down/up [C] down/up [F1] down/up
Let’s jazz it up a bit…
On the last [F1] keep that position but add in and remove your third finger (3) on the “C” string, third fret.
So, we’re going from [F1] to [F7] on alternate strums.