In Italy this sandwich is called pan bagnato, in Provence pan bagna. Either way, it means ?soaked bread? and that?s the secret: to let the flavors soak into the bread. Wrap in parchment paper to carry; the unfolded paper makes a portable placemat.
Slice baguette in half crosswise, then slice each half lengthwise in two, making bottom halves larger. Pull out and discard the insides so you have hollow bread shells. In a measuring cup or small bowl, whisk together vinegar and mustard. Whisk in olive oil until emulsified, then season with pepper. Brush some of the vinaigrette over the insides of the bread shells.
In a bowl, stir together the tuna, capers, onion, and olives; stir in the remaining vinaigrette until well combined. Mound tuna evenly in the bread shell bottoms. Arrange tomatoes and basil leaves over tuna, then put tops of bread on. Squish down to compress ingredients: you want the bread to get soaked with the flavors. Wrap tightly in plastic wrap and parchment to transport. If made ahead, refrigerate up to 4 hours, wrapped.