I fly a lot and my experience for trips like this is, shop around and get the best price possible using multiple web sites, then when you find a reasonable price book it. The small amount you can save waiting is useless if there are no more seats left.
Flights run very full these days. The routes to Europe in the Summer are typically very full with 'tourists' plus the usual business travelers. The chances a sale make come along are small, and if it does, you can always ask for a credit or refund on your fare if that happens.
The worse case scenario is you wait for a sale, seats fill up, you get forced to travel on days you don't want or worse yet no seats at all, then have to cancel your trip!!
So....hope that helps! Have a great trip!