Combine the red onion and red wine vinegar in a small bowl and let sit for 15 minutes, stirring occasionally.
In a large bowl, combine the tuna, celery, fennel, parsley, capers, olives, ¼ cup olive oil, lemon juice, and fish sauce or anchovy. Season with salt and pepper.
Drain the onions and add them to the tuna mixture, tossing to combine.
Divide the tuna salad evenly among the 8 toasted bread slices. Top with arugula and serve.
