TLDR: carriers using the 1st fighter type originally worked, now the fighters just fly around the enemy ship without firing.
In my current game I began experimenting with carriers (the previous times I'd tried them they were bugged). Built a couple of carriers, stuck an escort ship with them, and sent them into battle. They easily destroyed a larger enemy fleet.
Time to build carriers, right? So I built them...a lot of them. Peace was declared right after my experiment, so I continued building them. Now I'm at war again, using medium-sized carriers with 5 modules each. I use one or two large escort ships with max jamming. Now, though, the fighters just fly around and do nothing. Resolving the battle or quick battle (my 7-20 ships vs their 1) results in my entire fleet destroyed, except for the occasional 2 surviving carriers. The quick-resolve magically destroys my two invincible escorts which are pretty much immune to enemy fire when watching the battle.
My carriers are capital, jammer/defense are escort. I don't recall the enemy ship role.