There is no functioning market for international flights. A significant amount of the global fleet is still grounded. This is in total contrast to the domestic market, in which the fleet and crew are being reactivated.
Airfares normally vary because the airlines use yield-management software that balances remaining capacity vs. price history. If a flight gets full, prices go up. If a flight gets full really fast, you can put in a bigger plane or add a flight, and capture that demand. All that has been out the window for a year; flights were performed to 1) maintain critical infrastructure, 2) move cargo 3) maintain flight crew certification. As I said above, "normal" is expected to be coming back for the summer--only for domestic flights. The US still disallows non-citizens to enter. Europe's policy for vaccinated Americans will add some demand, but no family is fully vaccinated, since nobody under 16 is. And no vaccinated Europeans are welcome in the US. (watch for this, but it's getting to be too late for summer plans to be meaningful)
So, pandemic rules are still in effect for international flights, and will be until coordinated, or at least bilateral, travel rules are enacted. I flew back to the US last May, and was happy to pay "full" coach fair. Most of the air crews for widebodies have been grounded for a year. After 3 months, they need to go through re-training to get recertified, which takes months. The planes also need extensive maintenance to be ready to fly, and those facilities will become a bottleneck. Given the publicity around the European vaccination policy, get your ticket now while you can, as the airlines' ability to adjust up for demand will be very, very limited.
Get your deals once you are there. I'm sure every hotel, restaurant, vendor, and venue will be very welcoming and grateful.