Originally Posted by
findark
As xliioper noted, from JFK specifically there are usually pretty low fares available most of the year, although July/August remain good times if you actually want to travel then because of the lull in business.
The more general answer to the question is that, absent GUCs, just paying cash for a Z fare is going to be the easiest approach.
Flying partners AF/KL may be another option as they seem to have more reliable day-of-departure upgrade offers. Although pricing can apparently vary based on whether or not you have taken an offer in the past. As noted in thread below, yield optimization is tricky business and the airlines don't want to make it too predictable to get business class seats on the cheap.
KLM uses individual code system to determine upgrade price
One thing that is pretty predictable is that if you are booking shorter duration stays to EU that don't include a stay over a weekend period, you will likely only see higher business class fares due to the minimum stay requirements on cheaper roundtrip fares. This is a form of "fare discrimination" against business travelers who tend to make shorter duration trips and want to be back home by the weekend.