Preheat oven to 350°F. Line a large sheet pan with parchment paper and set aside. Dice the chicken. Finely dice the shallots and celery. Grate the carrots on the large holes of a grater. Shred the cheese.
Add the chicken, shallots, celery, carrots, and 1 cup (82g) cheese to a large bowl. In a separate bowl, combine the sour cream, mayo, Cajun seasoning, garlic powder, paprika, and a pinch of pepper. Whisk until smooth. Pour sauce over chicken and veggies and gently stir until everything is combined. Taste and adjust to personal preference, adding more Cajun seasoning if desired.
Slice a loaf of French bread into thick slices, about 1 to 1-1/2 inches thick. Place bread slices on the prepared sheet pan. Add 1/3 cup (82g) of the chicken mixture onto each piece of bread. Smooth into an even layer with the back of a fork. Add 1 and 1/2 tablespoons cheese to the top of each chicken melt to use the remaining 1 cup of shredded cheese.
Bake for 8–10 minutes or until cheese is melted on top. Remove from the oven. Garnish with fresh herbs and, if desired, a few thin slices of Roma tomato (my favorite!). Add a drizzle of hot sauce if desired. Enjoy immediately.
