Make the pickles: In a saucepot, combine both vinegars with ½ cup water, sugar, and salt. Bring to a boil to dissolve sugar and salt. Remove pickling liquid from heat and allow to cool to room temperature.
Meanwhile, peel carrots to form ribbons. Transfer carrot ribbons to a jar and set aside. Chop celery and add to a second jar. Divide pickling liquid between two jars and allow carrots and celery to pickle for at least 24 hours.
Make the chicken salad: In a mixing bowl, add the mayonnaise and spices and stir to combine. Add the leftover fried chicken and stir to combine. Season with salt and pepper.
In a small bowl, combine pickled carrot and celery with 1 tablespoon olive oil and season with salt and pepper.
Serve chicken salad on rustic bread topped with pickles.