Bring a medium saucepan filled with enough water to cover 4 large eggs to a simmer. Add the eggs, adjust the heat, and simmer for exactly 12 minutes. Transfers the eggs to an ice bath to cool. When cool enough to handle, peel the eggs.
Meanwhile, whisk together the olive oil, mustard and vinegar in a medium bowl. Chop the olives and add them to the bowl. Add the tuna with the oil. Thinly slice the red onion and add it to the bowl. Season with salt and pepper. Gently toss the ingredients together.
Slice the baguette in half lengthwise. Drizzle each half lightly with olive oil. Top both halves of the baguette with the tuna mixture. Slice the eggs and top the tuna mixture evenly with the slices. Sprinkle the eggs lightly with salt and pepper. Top with arugula. Carefully flip the top half of the baguette onto the bottom half. Cut into 4 to 6 pieces and enjoy right away, or wrap the whole loaf tightly in plastic wrap and refrigerate, slicing into sandwiches when ready to serve.