Heat 1 tablespoon of the oil in a large saucepan over medium heat. Add the onion and cook, stirring occasionally, until soft, 5 to 6 minutes.
Add the garlic and sweet potato and cook, stirring, for 1 minute.
Add the broth and lentils and simmer, covered, until the lentils are tender, 20 to 25 minutes. Season with ½ teaspoon each salt and pepper.
Meanwhile, heat the remaining oil in a skillet over medium-high heat. Season the fish with ¼ teaspoon each salt and pepper. Cook until opaque throughout, 3 to 5 minutes per side.
In a bowl, whisk together the mustard, wine, and tarragon. Divide the lentil mixture and fish among plates and drizzle with the sauce.