How to Make It
Stir together all rémoulade ingredients in a bowl. Cover and chill until ready to serve, up to 3 days.
Place buttermilk in a large bowl; add chicken, and submerge in buttermilk. Cover; refrigerate at least 3 hours or up to 8 hours.
Stir together flour, salt, black pepper, garlic powder, onion powder, paprika, and cayenne in a shallow dish. Remove chicken from buttermilk; discard buttermilk. Dredge chicken in flour mixture, shaking off excess, and place in an even layer on a wire rack set inside a rimmed baking sheet. Let stand at room temperature 15 minutes.
Place fennel and onion in a medium-size heatproof bowl; set aside. Bring 1 cup water, vinegar, sugar, and salt to a boil in a small saucepan over high, whisking occasionally. Pour vinegar mixture over fennel mixture; let stand 10 minutes. Add peaches; toss gently to combine, and let stand 10 minutes. Drain, discarding vinegar mixture.
To fry chicken, pour oil to a depth of 2 inches in a large Dutch oven; heat to 350°F over medium-high. Working in batches, carefully add chicken thighs to hot oil; fry until golden brown and cooked through, 6 to 8 minutes, turning occasionally and maintaining an oil temperature of 325°F. Transfer to a wire rack set inside a rimmed baking sheet to drain; sprinkle evenly with salt to taste.
Spoon rémoulade onto 4 plates. Top with pickled peach-fennel salad and fried chicken. Garnish with fennel fronds.