Combine shallots and tarragon vinegar in a small bowl; let stand 10 minutes. Add mayonnaise, mustard, and tarragon; stir well to combine. Reserve 3 tablespoons mayonnaise mixture. Add chicken to remaining mayonnaise mixture; stir well.
Spread about 2 teaspoons reserved mayonnaise mixture on bottom half of each baguette portion. Top each with 1 lettuce leaf. Divide apple slices and shaved cheese evenly among sandwiches. Top each sandwich evenly with 1/2 cup chicken salad and remaining bread half. Chill until ready to serve.
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