Honestly, yeah, an XCOM character would be pretty cool to see.
An XCOM Soldier could have maybe a laser or plasma assault rifle. Cover and Overwatch are vital to the reboot's gameplay, so of course there could be something for those. You could also give them stuff like the Arc Thrower, or the GREMLIN. I mean, part of XCOM's appeal is that you go from "military men with machine guns" to "superhero psions with spazers" - and if we can only pick one of those, I know which one's more exciting.
Speaking of psions, maybe a Psi Operative, specifically, would be best. I guess in XCOM 1 they're just "Psionics", but whatever. Their moveset could include most of the same stuff a regular soldier's could (they are, after all, a subtype thereof), but you could also get Sectoid-like psionic abilities that are even more specifically XCOM.
Though I wonder if this is one of those situations where the character pick is somewhat up-in-the-air. XCOM is about aliens invading Earth, so maybe a Sectoid would be a better pick...
I dunno, this is an interesting rabbit hole to go down.