Something similar happened to me one time. I made a FaceTime call, and it connected to a complete stranger. We both freaked out.
I had an old, stale cell phone number still attached to the person I was calling. I suspect, but could not verify, that the number had been re-used and the new owner attached it to a different Apple ID. FaceTime decided for some reason to place the call to the wrong Apple ID.
I deleted the old phone number. Since then, I've never had any trouble making this FaceTime call.