Preheat the oven to 500 degrees F. Butterfly the chicken: Remove any innards from the chicken. Put the whole chicken breast-side down on a flat surface. (I like to put a kitchen towel underneath the bird to prevent the chicken from sliding around as I work.) Find the backbone running down the center. Use a pair of sharp poultry shears or scissors to cut up along the backbone on one side and then cut along the other side. Remove the backbone and save it to add to chicken stock. Flip the bird over, breast-side up. Gently press down on the breast meat to open the chicken up and flatten it. The breastbone will break as you press. The chicken should now sit almost flat.
Cook the chicken: Season the chicken on all sides with salt. Put the chicken skin-side up on a rimmed baking sheet lined with a rack, put the pan in the center of the hot oven and cook undisturbed for 20 minutes. Then lower the oven temperature to 450 degrees F and cook for an additional 30 to 35 minutes. The chicken is ready when an instant-read thermometer inserted in the thickest part of the bird registers 155 degrees F to 160 degrees F. Remove the chicken from the oven and allow it to rest for at least 10 to 15 minutes.
Meanwhile, make the mustard vinaigrette: Whisk the dijon and grainy mustards with the vinegar, 1/2 teaspoon salt and 1/8 teaspoon pepper in a small bowl. Gradually whisk in the canola oil and 1 tablespoon cold water. Taste for seasoning.
Serve the chicken: Transfer it to a cutting board for carving. Serve with the mustard vinaigrette.