The cheapest time to fly to Europe isn't far away. Actually, if you compare airfares throughout the year, you'll find that the cheapest time to fly to Europe is in early spring. In other words, you'll find the cheapest flights departing in February, March, and early April. That's the least busy time of the travel season in most of Europe (along with late October and sometimes November) and will get you the cheapest flights and hotel rooms. Keep in mind that attractions might not be open, and the weather may not be exactly right for a tan at the beach. If you don't mind that, then this is definitely your time to fly.
Compare flight prices here from all major travel sites at the same time (and don't forget to try out different dates for maximum savings).