Combine vinegar, shallot, mayonnaise, mustard, ⅛ teaspoon salt, and ⅛ teaspoon pepper in bowl. Slowly whisk in oil until thoroughly incorporated; set aside.
Cook bacon in 12-inch nonstick skillet over medium heat until crisp, about 8 minutes. Using slotted spoon, transfer bacon to paper towel–lined plate. Pour off all but 1 tablespoon fat from skillet. Heat fat over medium-low heat. Fry eggs, covered, until whites are just set, 2 to 3 minutes.
Meanwhile, toss frisée and romaine with dressing and divide among individual bowls. Top each salad with fried egg and bacon. Season with salt and pepper to taste. Serve.
