Place the eggs in a single layer in a saucepan and cover with cold water by about 1 inch.
Bring the water to a boil over medium-high heat. Once boiling, cover the saucepan, remove it from heat, and let the eggs sit for 10 minutes.
Drain the hot water and transfer the eggs to a bowl of ice water to cool for 5 minutes.
Peel the cooled eggs and chop them into small pieces.
In a medium bowl, combine the chopped eggs, mayonnaise, Dijon mustard, lemon juice, salt, and black pepper. Mix well.
Add the chopped celery, red onion, and chives to the egg mixture and stir to combine.
Slice the baguette lengthwise without cutting all the way through, creating a hinge.
Evenly spread the egg salad inside the baguette.
Cut the baguette into 4 equal portions and serve immediately.