Combine vinegar, Champagne, shallots, ginger, salt, and pepper in a medium bowl, and whisk well. Transfer 1/4 cup of liquid to a small heatproof bowl, and sprinkle gelatin on top. Let stand to soften, 5 minutes.
Meanwhile, bring a small pot of water to a boil, reduce to a simmer, and set bowl with gelatin mixture in hot water. Heat, stirring, until gelatin is dissolved. Return to remaining liquid, and whisk to combine. Pour into a 5-by-9-inch loaf pan lined with plastic wrap and refrigerate until set, at least 4 hours or up to 3 days. Remove from pan, and cut into circles with a 1/2-inch round cutter.
Place oysters in bed of ice, and top each with 2 circles and a sprig of tarragon.