Let the Brie cheese sit at room temperature until softened.
In a bowl, mix the softened butter, minced chives, minced parsley, Dijon mustard, and grated garlic. Season with salt and black pepper to taste.
In a separate bowl, toss the arugula with lemon juice. Season with salt and black pepper.
Spread the herb butter mixture evenly on the bottom half of the French baguette.
Layer the baguette with sliced deli ham, softened Brie cheese, and seasoned arugula. Top with the other half of the baguette to form the sandwich.
To make the chia fresca, begin by squeezing fresh lemon juice and set it aside. Measure the maple syrup or honey, chia seeds, and a pinch of salt.
In a medium pitcher, combine the lemon juice with maple syrup or honey and stir well. Add the chia seeds and salt, then slowly pour in the still water while stirring gently to combine. Let the mixture sit for a few minutes so the chia seeds can hydrate.
Pour the chia fresca into glasses and garnish each with a sprig of fresh mint.
Serve the jambon beurre sandwich with carrot sticks, hummus, pickle spears, and the chilled chia fresca on the side.