In a large, deep sauté pan or a large, wide saucepan, melt butter over medium-high heat. Add shallots, garlic, and herbs and cook, stirring, until shallots are soft and fragrant, about 1 minute. Add wine, heavy cream, salt, and pepper, and bring to a boil.
Increase the heat to high, add the mussels, cover the pan, and cook, shaking pan occasionally, until mussels have opened, 6 to 7 minutes.
Remove the pan from the heat and discard any mussels that have not opened. Transfer mussels and liquid to a large, deep serving bowl and garnish with chopped parsley. Serve immediately with warm, crusty bread and Pommes Frites for dipping.