Originally, I went with a hard G, as in "go away!"
But I realized that was wrong, for a few reasons.
1) As someone else pointed out, G is usually soft before an E, such as in "generation" or "genuflect." However, we all know D&D and fantasy names often don't follow English structure. That said...
2) The genasi, as a concept, were originally descended from genies, and that (I'm pretty sure) is where the name came from. As such, a soft G--so it's pronounced "jenasi"--makes much more sense in-character as well.
So I pronounce it:
"jen" as in "Jennifer" or "generation"
"oss" as in "cross"
"ee" as in "Whee!" or "free."