Mix the carrots, vinegar, 2 tablespoons sugar, and 1/2 teaspoon salt in a large bowl. Let stand while preparing the rest of the sandwiches, stirring occasionally.
Mix the turkey, cilantro, garlic, fish sauce, sriracha, remaining 1 tablespoon sugar, and 1 teaspoon each salt and pepper in a large bowl with your hands until very well-mixed. Form the mixture into patties to match the dimensions of the baguette pieces (about 5 inches long, 2 inches wide).
Spread 1 tablespoon mayonnaise on the cut sides of each baguette piece. Place some cilantro sprigs on the bottom halves.
Heat 1 tablespoon oil in a large cast iron skillet over medium-high heat. Add 4 of the patties and cook, turning once, until browned and cooked through, about 7 minutes. Transfer to 4 of the baguette bottoms. Repeat with the remaining oil and patties. Drizzle sriracha on the patties, if desired, then top with the cucumber. Drain the pickled carrots and scatter over the cucumber, along with more cilantro sprigs. Sandwich with the baguette tops and serve immediately.