Don Firth wrote;

"Yes, the time signature definitely influences the note structure of a melody. "

I agree, but I also think the rhythm of the words can, and should influence the choice of time signature.

Some years ago, I was doing a music evening class and was set a task to write music to some existing words. I got my younger daughter, who was about 12 at the time, to write me a couple of poems (she's good with words). She came up with one about Christmas and all the jollification around Christmas and one about Winter Weather.

The Christmas poem just seemed to bounce along and I ended up writing a tune in 6/8 simply because the rhythm of the words fitted that time signature and the whole effect was nice and bouncy. The Winter Weather poem was altogether more sombre and I ended up writing a tune in 4/4 but again the shape of the poem and what was being said very much influenced the melody, not just the rhythm in this case, but the shape of the melody as well.