Place fish fillets in a baking dish. Drizzle 2 tbsp each of olive oil and lime juice over the fillets and season fish with salt. Marinate at room temperature for 10 minutes.
While the fish is marinating, in a large mixing bowl, gently combine the avocado, mango, onion, jalapeno, cilantro, basil, remaining olive oil and lime juice. Add cumin, ½ teaspoon salt and pepper and set aside at room temperature.
Brush grill rack with melted coconut oil (you could alternatively cook the fish in a cast iron pan over the grill). Grill fish until just opaque in the center, about 5 minutes per side. Transfer fish to plates and break fillets up a bit, serving on corn tortillas. Spoon salsa over fish and squeeze a lime wedge over each. Serve warm and enjoy!