In the US, a common tactic (if you prefer regular airlines or want to collect those frequent flyer miles), is to find out when a budget airline flies the route you want, then check to see if your preferred carrier flies at about the same time. Usually those are the flights where you will get the deepest discount, because they need to compete with that budget carrier.
Does this work in Europe, or are the fares so ridiculously low that none of the majors even try to compete?