Tachanun is not said when there is a Chatan in the minyan. However, on a fast day, Tachanun is usually said with Selichot. So if there is a chatan in a minyan on a fast day, would you say Selichot without tachanun?
According to Mishnah Berurah commentary on O.C. 131:5 comment #27, if a chattan is in shul on a fast day, they say Selichot, but do not say Tachanun.