Heat broiler. On a broilerproof rimmed baking sheet, toss the baguette pieces with 1 tablespoon of the oil. Broil until golden, 3 to 4 minutes.
In a large bowl, combine the beans, pickles, onion, vinegar, the remaining 3 tablespoons of oil, ½ teaspoon salt, and ¼ teaspoon pepper.
Fold in the toasted baguette.
Divide the mixture among bowls and top with the tuna.