Kent, I have not been to the self serve style of place, but I recommend going to an outdoor market and purchasing some prepared food there. I visited the Grenelle-Motte Piquet marche, at the Motte-Piquet metro and purchased some cooled potatoes and shaved ham cooked in a mustardy sauce, omg yummmmy. My friends had other dishes. They were hot and packed in to go containers; we strolled to the Seine and sat in benches to eat. So heavenly and such a lovely picnic spot.
Many other markets had cooked food. Markets are my favourite thing, so I frequent them. Some have already made sandwiches, others make things to order. You could buy cooked chickens too with potatoes cooked in the dripping fat, really delish. I am gluten free, so I am a bit challenged at times. I often buy cheese and fruits, olives and nuts at the market. Many Parisiens eat their lunch outside in parks. I have packed a small lunch ir purchased of it at the market and joined them. Such a great experience.
Monoprix often has many packaged foods for lunch, like salads of different types. Of course, you can pick up a dessert at a patisserie. Markets have marvelous dried fruits, more than I have ever seen anywhere.
I often each lunch and sometimes dinner in brasseries which are often more informal. La Terrasse which is by the Ecole Militaire metro, near the Eiffel tower is one of my faves. Sit outside if it is warm and you can tolerate smoking. I often stay near there and have eaten many a meal or just had a drink and people watched as locals come home from work.
Enjoy the food. Try as many cheeses as you can.