Make the vinaigrette: Stir together the shallot, mustard, honey, vinegar, 3/4 teaspoon salt, and pepper to taste in a bowl. Whisk in the olive oil.
Thinly slice the zucchini and squash lengthwise (with a mandoline, if you have one, or a vegetable peeler), then thinly slice the beets and mushrooms. Drizzle with the vinaigrette and toss. Sprinkle with the chives, chervil and tarragon. Season to taste with salt and pepper.