There is a food board called HungryOnion.org with an excellent Paris section. Many American visitors ask questions of each other and those that live there & get great recommendations (& discussions) on all types of restaurants, wine bars, food shops & neighborhood markets. Take a look - you have some time.
Before I answer your question, I have a couple of my own: first, does your request for "not fancy" mean "not expensive" or just not too upscale of an environment. And, what is your price range? Secondly, although the 3rd is full of small places, it is also adjacent (& walkable) to the 11th, which is a restaurant Mecca. And, of course, as you know, it's easy to get around Paris by bus/metro as well, so I wouldn't put much off limits if I were you. Are you open to other areas?
We just came back from a month's stay (not our first) &, depending on your answers, I can give quite a few suggestions.
And, off topic from restaurants, I just wanted to mention that the Paris History Museum finally opened a year or so ago
https://www.carnavalet.paris.fr/ & is great. The "sign room" alone is worth the visit. Right there in the Marais.