Cut the codfish into 1-inch pieces. Drizzle 2 tablespoons of oil over codfish. Season with salt, pepper, thyme, and tarragon. Cover, place in refrigerator, and marinate for 1 hour.
Preheat oven to 400 degrees F.
Remove herbs from the codfish. Warm a skillet with a little olive oil and add the codfish. Next, add the shallots and cook until tender. Place the cooked codfish in the bowl of a food processor and using short pulses, mix lightly. Add the cooked potatoes and pulse lightly. Add the remaining olive oil and pulse lightly. Adjust the seasoning with salt, pepper, minced garlic, and cayenne pepper.
Place the baguette slices on a cookie sheet and brush them with olive oil mixed with a touch of minced garlic. Bake them until light golden brown.