I stumbled upon a radio interview with an experienced travel agent and travel writer in my area. His advice on inexpensive foreign travel was to look to other non-airfare expenses to cut costs.
His rational is that with the limited number of airline cartels flying between the US and Europe, and their expertise at filling planes to capacity thus eliminating 'fire sale' prices on tickets, airfare is not the best area to find economies. And often the economies are false, requiring tortuously long flights and lay overs, wasted vacation days, and extra expenses for hotel rooms, cabs, and other forms of transportation.
He pointed out that even shoulder and off season airfares are higher as the airlines have learned to park planes and not fly with empty seat.
He recommends looking for deals on rooms as there are hundreds if not thousands of hotels competing in major cities, and services like Airbnb adding to that competition. He also recommends looking for making your own meals with picnics, meals in the hotel room, and walking a few blocks out of the main tourist areas to restaurants that don't routinely saver mostly tourists.
I have found that to be true so far. I could knock $300 off of the airfare if I wish to give up a day or more of my trip to travel time and exhaustion, and pay for an additional night's room and transportation to another city with lower fares. Sorry, that's too big a price to pay so I can brag about getting a lower fare.
I have one more tip of my own for the rest of you: Wait until I buy my tickets. No doubt prices for the same exact flight will drop by at least 15% the next day.