I'd say you have three possibilities here, one of which I have done myself and succeeded at:
1) attack them immediately upon their awakening, preferably alongside one or two large empires. The sooner, the better.
2) take advantage of circumstances to defeat them, such as a galactic crisis.
3) submit to them, gain power alongside them, and then take them out when you're eventually able to surpass them (which WILL happen eventually, if you keep pressing forward).
The first one was the one I did the first time I had to take them on, and it worked out surprisingly well! In actuality though, I was in a defensive pact with a large xenophilic empire (ironic since I was a xenophobe) and I got pulled into the war by the FE. What I did was thus: Set my fleet to be point, and waited. The FE is a bit dopey sometimes and doesn't often make the first move, which some would consider to be a smart move. I kept a scout near their three fleets and waited for just one of them to move. I goaded a fleet out using surgical strikes, and then our ships swooped in and took them out. Bish bash bosh, a third of their navy destroyed. One climactic battle with the remainder of their navy later and we'd cut them down to a size they could not recover from.
I personally think the doomstack is what makes FEs so imbalanced. Hopefully Wiz will be looking into this issue in the near future, for as cool as the supermassive fleet is it's really imbalanced and annoying to have to fight.