Sprinkle the sturgeon with 1 tablespoon of the vinegar and refrigerate for 10 minutes. In a large, heavy skillet, combine the remaining 2 tablespoons of vinegar with the water, bouquet garni and shallot and bring to a boil. Season the poaching liquid lightly with salt and pepper and add the sturgeon fillets. Cover tightly and simmer over low heat, turning once, until the fish is barely cooked through, about 8 minutes. Transfer the sturgeon to a large plate. Strain the poaching liquid into a bowl.