In small bowl, combine mayonnaise, 2 tsp. tarragon vinegar and dried tarragon in a small bowl. Cover and refrigerate.
Place sliced vegetables in a zip-top plastic bag or large baking dish, season with salt and pepper and drizzle with the 1/4 cup of olive oil and 1/4 cup of tarragon vinegar. Set aside for a few minutes to marinate.
Prepare and preheat two sided grill. Place vegetables on grill and cook 3 minutes, until tender. Reduce grill heat to medium-low. Brush French bread slices with olive oil and grill 2 minutes per side, until golden brown.
Spread each slice of bread with the tarragon mayonnaise, then form sandwiches with the grilled vegetables. 2 sandwiches