Make the poached chicken: Bring water, wine, chicken, fennel fronds, tarragon, salt, coriander, and peppercorns if desired, to a boil. Reduce heat, and simmer for 5 minutes. Remove from heat. Cover, and let stand for 35 minutes to cook chicken through. Shred chicken; discard skins and bones.
Make the vinaigrette: Whisk together oil and vinegar, and season with salt and pepper.
Make the salad: Combine lettuce, vegetables, apple, and tarragon in a large bowl. Add chicken. Drizzle with some vinaigrette, and toss. Serve remaining vinaigrette on the side.