Thoroughly wash and dry all the herbs. As you prepare the herbs, put them in a salad bowl. Trim the stems from the sorrel and cut the leaves in half. Strip off the leaves of the green basil, the opal basil, and the tarragon and discard the stems. Take sprigs of chervil and dill from the main stems and discard the stems. Cut the chives into 3-inch lengths.

To make the vinaigrette: In a bowl, whisk together the vinegar, lemon juice, shallots, and a lime salt and pepper. Still whisking, add the olive oil in a thin stream. Pour half the vinaigrette over the herbs in the bowl and toss gently until all the leaves are lightly dressed. Taste the salad and add more vinaigrette to taste.