In addition to early June, the 4th of July and late August into September are good times to hop on a plane. At the opposite end of the spectrum, July 1 is the most expensive day to travel to Europe this summer. The study also found booking 99 days in advance of the trip is when you're most likely to find the cheapest fares.
In addition to finding the cheapest days, CheapAir.com says travelers should adjust their expectations when flying to Europe in the summer. It's a more expensive time to travel. It also recommends looking at mixing and matching flights, considering flying into smaller nearby airports, and researching local holidays so you're not unwittingly flying into a city during a busy holiday weekend.