In a large Dutch oven or straight-sided 12-inch saute pan, heat the olive oil over medium heat. Add the shallots and garlic and cook until softened, about 2 minutes. Add the white wine and bring to a boil. Season with salt and pepper. Add the mussels, cover and steam until open, about 3 minutes. Using a slotted spoon, transfer the mussels to a large serving bowl.
Add the creme fraiche, parsley, butter, chives and mustard to the remaining cooking liquid and bring just to a boil while stirring to combine. Pour the sauce over the mussels. Serve with French fries.
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