Combine grapeseed oil, lemon juice, garlic, vinegar, dill, oregano, and coriander in a 1-gallon resealable plastic bag. Taste marinade; add desired amount of salt and pepper. Add chicken and seal the bag. Shake gently to ensure chicken is evenly coated with the marinade.
Marinate the chicken in the refrigerator for 3 to 4 hours.
Make white sauce by whisking mayonnaise, yogurt, vinegar, parsley, lemon juice, honey, salt, and pepper together in a bowl. Refrigerate until serving.
Preheat the oven to 450 degrees F (230 degrees C). Spread french fries on a rimmed baking sheet.
Remove chicken from the marinade and season with more salt and pepper. Heat olive oil in a large cast iron skillet over medium-high heat. Cook chicken until browned on one side, about 5 minutes. Flip and continue cooking, reducing heat if needed, about 5 minutes more.
Meanwhile, bake fries in the preheated oven until light golden in color, 9 to 12 minutes.
Shred chicken or cut into small chunks. Divide fries among serving bowls; top with chicken. Drizzle while sauce over the top.