Put the olives, peppers, garlic, tomatoes, and parsley in the bowl of a food processor and pulse until finely chopped. Transfer to a bowl and add the lemon and tuna. Stir well and season with salt and pepper.
Slice the baguette in half cross wise and then lengthwise, so you have four pieces. Put them on a sheet pan and divide the basil leaves between the slices.
Top with the tuna mixture.
You can eat this sandwich as is, or you can make a more traditional French “picnic style” sandwich by wrapping the sandwiches tightly with plastic and pressing them with something heavy — a sheet pan topped with a heavy skillet, bricks, canned goods — anything heavy enough to press the sandwich. Doing this will saturate the bread with the oil mixture, and press the tuna salad so that it’s easier to eat. Press for several hours in the fridge before enjoying.