Chill oysters, rock salt, and two plates.
Combine the Champagne, shallot, and tarragon stems in a small saucepan over medium-high heat and bring mixture to a brisk simmer for about five to six minutes, until the liquid is reduced to two tablespoons. Strain and discard shallots and tarragon stems. Cover and chill.
When ready to serve oysters, whisk the oil into the reduction. Reserve 12 tarragon leaves for garnish. Add remaining tarragon and chervil leaves to the dressing.
Place cold rock salt on chilled plates to a depth of 1/2 inch. Shuck oysters and arrange them in the salt. Peel and thinly slice a quarter of the avocado. Lay one slice over each oyster and drizzle dressing over the top. Lightly season with sea salt, garnish with one of the reserved tarragon leaves, and serve.