Honest to god, I've never eaten your typical 'american' tuna fish sammy. It looks and smells vile to me (I'm employing hyperbole for effect, btw). However, when I first visited Paris, I got caught famished before visiting Père Lachaise Cemetery (quite beautiful, by the way - with many famous people buried there) and found a small place closeby that sold sandwiches. The only one they had left was tuna since it was late. On a baguette, and it changed my view ever since. It had chunky pieces of tuna (I believe it was in fact, canned), just the right amount of mayo (less than here), and finely diced vegetables. Unlike the mash/ paste homogenous stuff deli's and diners make here in the US.
Since then, canned "tuna" for me is simply a vehicle for everything else. And the mayo as a binder. Usually tuna in oil (sometimes add some of this oil), but in water is ok too. I use the brand Tonnino in a can, not the jarred one. I usually use finely diced celery, red onion, carrot, and sometimes cucumber. Yesterday I used finely sliced fennel. Sometimes fresh oregano, maybe thyme, parsley, lemon zest. Sometimes a squirt of dry white wine. Sometimes hard boiled egg. Definitely on toasted bread or sometimes in a pita with a green leaf lining - romaine or spinach or rocket. The type of vegetables and bread also depends on what I have, but sour dough, whole wheat, rosemary loaf, it's all good. The only thing I don't seem to use is mustard, but now that many of you have listed it as an "almost requirement" I'm going to try it (and Worcestershire sauce as well). The amount of veggies depends on the tuna. Each separate veg is the same size pile as the tuna, so if I have four veg, then it's one fifth tuna. The one thing I noticed is that if you add salted chopped tomato, it will add a lot of moisture to your sammy and make it drip and runny. Drier results are achieved by adding a slice at the end. I also don't mash it into a paste. I created the dressing in a bowl, add the veggies and toss thoroughly. Then I add the tuna and fold it in, retaining some chunks. I've also altered the base tuna using various ingredients like chipotle, cumin, pimenton, fresh basil or cilantro, and even fish and/ or soy sauce. Not all of them together, though! : )
It has now become a lunch staple that is open to all kinds of variations.
Sorry for the long post. . .