A few things.
(1) Don’t know if you are in the U.S., or where, but there’s a distinction to be made between first class domestic, and internationally. The former are not that much nicer seats or amenities, and hence tend to be given away a little more liberally. (But it depends who you are – if you are in an airline amenity/frequent flyer program, and have high status therein, you might automatically upgrade, for free; but if you’re not in said program, you might find that all the seats were given away automatically to such frequent flyers, so there are none on the market).
International first class tends to be much plusher (and more desirable, because longer flights). So the airlines guard that more carefully, as putting premium-paying business travellers in FC is an absolute cash cow for them. On the plus side, they don’t give these seats away for free even to their own frequent flyers (but, you will face competition from FFs still, as they may have the ability to upgrade, though it’s usually still not super cheap).
Sometimes, you are also facing competition from deadheading crew.
(2) Airlines DO occasionally have first class sales that would allow you to fly trans-Atlantic for, say, $1500 (these tend to occur at slack travel periods or to less-popular destinations).
(3) (RISKY BUT PEOPLE DO IT) I quickly checked the SDMB TOU and convinced myself it was not un-kosher to mention this, as the worst it involves is an arguable breach of contract, not anything in any way illegal. Services exist (Google “buy airline award tickets”) that will sell you “discounted” first class tickets that they acquire by paying frequent flyers (strangers) to book a ticket, using their excess miles to secure an award ticket in your name. The airlines claim that this violates their FF TOU and that if they catch you doing it, they’ll void out the ticket and confiscate the miles, and you’re likely up a creek, as I doubt the award-broker will refund the money you paid him (given that the FF who sold him the miles sure isn’t going to give back what he was paid). How risky this is, I do not know.
(4) I came across this site, which claims to offer heavily discounted premium seats on international flights. I have no idea how legit it is, but have a look.
(5) People have passed along to me some copies of this guy’s newsletter.
http://www.flightbliss.com/firstclassflyer/
It’s decently-researched, and he does a lot of pretty smart legwork in tracking down glitches in the system or (often transitory) angles or market aberrations that can lead to particular strategies for getting premium seats (usually on specific routes or airlines) at non-awful prices. Being a good capitalist, though, he charges for his legwork.