Eating mussels spread to France from Belgium where they were cheap and abundant along the Flemish coast. Although there are all sorts of ways to flavor the cooking liquid, the basic technique for preparing mussels is straightforward.
Mussels are alive when you buy them, so keep them chilled and cook them as quickly as possible after purchase. Before cooking, sort through the mussels and discard any that are not tightly closed or do not close when tapped against the countertop and ones with chipped or cracked shells. Quickly sort the mussels a second time as you remove them from the pot, and discard any that have not opened. In short, the rule for mussels is shells closed before cooking, and shells open after cooking.

In a large pot over medium-high heat, warm the oil. Stir in the shallots and cook until tender, about 3 minutes. Stir in the garlic and cook until fragrant, about 30 seconds. Stir in the wine, cream, butter, tarragon, and season with salt.

Add the mussels, cover and cook 2 minutes. Stir the mussels, cover and continue cooking until they open, 4 to 6 minutes. Discard any mussels that do not open. Sprinkle with parsley and serve at once with the broth and some crusty bread.