Heat 1 tbsp. of the olive oil in a large skillet over medium-high heat. When the pan is hot, add the fish fillets and season with salt, pepper, and paprika. Cook the fish until firm and opaque, about 4-5 minutes on each side, and transfer the fillets to a plate to rest.
Wipe out the skillet, return it to the heat, and add the second tbsp. of olive oil. Add the sliced onion and bell pepper, stirring frequently, until they begin to soften. Add the zucchini and cook for another 1-2 minutes, until just tender. Stir in the carrot shreds and toss for just a few seconds before removing the pan from the heat.
Assemble the burritos by topping the tortilla with rice, fish, vegetables, tomato, avocado, cilantro, and a generous squeeze of lime juice. Wrap the filling tightly and serve immediately.