But I think they both should be fired for this reason: the entire school will have seen it and it will always get in the way of normal student-teacher relationships, not to mention teacher-administration and teacher-parent relationships. They simply won't be able to do their jobs and the students will suffer for it.
Unfair maybe but the students come first - at least they're supposed to.
But they can't discriminate based on gender. Firing her and not the fiance will very likely lose the lawsuit for them.