Heat grill to high. Sprinkle garlic with a pinch of salt and, with the flat side of a large knife, mash and smear the garlic to a coarse paste. Heat the oil in a stockpot on the grates of the grill, add the shallots and garlic and cook until shallots soften. Add the wine, bring to a boil and stir in the mussels. Cover the pot and cook the mussels until all of them have opened, about 6 to 8 minutes, discard any that do not open.
Remove the mussels with a slotted spoon to a large bowl. Bring the cooking liquid to a simmer and whisk in the butter. Season with salt and pepper, to taste, and stir in the tarragon. Pour the mixture over the mussels and serve immediately with grilled bread.
Brush cut side of baguette with oil, season with salt and pepper and grill, cut side down until lightly golden brown.