Balthier and Fran do not have a child!!! the child in the credits is Balthier/Ffamran being held by Cid.

whether or not they are together romantically is still a lil bit of a mystery altho it seems they are. as in Revenant Wings (SPOILER)theres a bit more tension between them and apparantely Balthier has been giving her flowers and trinkets and they like to spend time alone together a lot more than they did before. I think penelo suspects that stuff is going on there. And its not gross even if they did have a kid cos its established in Ivalice that Veira and Hume, Veira and flying thing, and Veira and Seeq can all have relationships.
(SPOILER)the villain is a veira who was in love with a hume, and Fran seems to take this to heart

but again they don't have a kid, or if they do they are doing a bad job at parenting it cos you never see or hear about it