Heat oil in a large saucepan over medium heat. Add carrots, onion, and celery and saute until tender, about 5 minutes.
Add Cajun seasoning, sweet potatoes, and broth and bring to a boil. Cover, reduce heat and simmer until potatoes are just tender, about 10 minutes. Add salmon and corn and simmer until salmon is just opaque in center, about 3 minutes.
Reduce heat to low, stir in half-and-half, basil and season with salt. Cook, stirring gently, until heated through.