Set the pan on the stove to medium-high heat. Add the andouille sausage and cook on both sides until it darkens slightly in color, about 5-10 minutes.
Lower the heat to medium and add the olive oil. Add the shallots and garlic and cook until softened, about 2 minutes.
Add the white wine and bring it to a boil. Season with salt and pepper. Add the mussels. Cover and steam until the mussels open, about 3 minutes.
Using a slotted spoon or sieve, transfer the mussels to a large serving bowl or several small serving bowls.
Add the crème fraîche (if using), butter, parsley, chives, and mustard to the remaining cooking liquid in the pan, stirring to combine. Bring just to a boil, then pour over the mussels.
Serve with French fries. Mayo for the fries and a hunk of crusty bread are also delicious.
