We see carnivores eating;
Breakfast Cereal (the "Art Of" book helpfully provides a list of ingredients)
The film's writer, Jared Bush addressed this issue (via twitter).
Q: Hey, can you tell me what do they eat? What would the carnivores eat? I'm really curious
JB: in Zootopia, carnivores eat plant-based proteins and insects.
Bug-burga is their favorite restaurant
Q. What about fishes? Do they eat those too?
JB: in early versions of the movie they ate fish (which weren't "evolved" and didn't talk) But it confused the rules of the world.
For the record, I've added punctuation because it would seem that neither party know how to use it.
And in this linked article, the film's directors offer us a little more info about what you can buy at this popular eatery.
[Byron] Howard and [Rich] Moore had to create a film where animals could live
together, those who would normally be prey and others who would be
predators. And in doing that, they also had to solve the problem that
the predators still need meat protein and would normally be eating the
prey. So the most popular fast food restaurant in Zootopia is
Bug-Burga, where protein can be found. Howard said, “In Bug-Burga, you
can get a grasshopper shake, cricket chips, or a cicada burger. And
it's all viable protein. In one scene where Nick is telling Judy that
she'll never be a real cop, you're going to go home and be a carrot
farmer, he takes part of a fence and moves it aside. If you look down
by his feet, there are Bug-Burga boxes in the litter on the ground.”
It is one of the only places viewers will see the restaurant noted in