We're still seeing excellent fares on United from nearly everywhere in the USA to Amsterdam, Paris, Rome, and other cities in France/Italy. Fares are in the mid $400s to mid $500s.
Update February, 7, 2:30 pm: It looks like these fares have finally gone back to their normal $1000+ on most routes. Congrats to all who booked these amazing fares to Europe. Sign up for alerts to get in on the next sale.
As this is unadvertised, prices may jump at any time. We suggest booking soon if you like what you see. Most third party booking sites have a 24-hour free cancellation policy so you'll have a day to figure out the details.
Travel is generally through mid-May and from mid-August onward, though some routes will have less availability. A 28-day advance purchase and a 7-night minimum stay is required. Some flights may be operated by Star Alliance partner airlines.
These prices are around what you'll find on the major booking engines. Lower fares may be found on some more obscure third party booking sites. Unfortunately, most United and American hub cities are excluded.
Even if your favorite airport (small or large) isn't listed, there may be a big price drop. Other cities in these countries are likely lower than normal as well.