Heat 1 tablespoon of the oil in a large skillet over medium-high heat.
Add the sausage and cook, turning occasionally, until cooked through, 10 to 12 minutes. Transfer to a cutting board and let rest 5 minutes before slicing.
Wipe out the skillet and heat the remaining tablespoon of oil over medium heat.
Add the carrots, onion, ½ teaspoon salt, and ¼ teaspoon pepper and cook, stirring occasionally, until tender, 8 to 10 minutes.
Add the beans and wine and simmer for 5 minutes. Fold in the sliced sausage and tarragon.