In Paris, you will find bistros and restaurants everywhere. They open early, you can have breakfast there, most serve food at noon and on evenings, but not all do both, that depends on the place and their usual guests. Most don't serve food at all hours, so it's lunch (12 to 2 or 3pm) or dinner (usually after 7pm), not much in between. Maybe a cake.
If you go in a classic bistro, you can stand on the bar or sit on the bar stools and the coffee is cheaper than sitting in the room on a normal table or on the terrace. Being on the bar means chatting with everyone, the barmen, the other guests, usually joking, most trying to speak English if you don't speak French. Just start with "Bonjour" and a smile to be polite.
Most bistros have wifi, ask for the code. Most bistros have newspapers to look up the wheater (last page) or some headlines.
Most restaurants and bistros serve a plat de jour, a dish of the day at noon. That's cooked specially on that day and is cheaper then it would normally be. Some places offer a "menu", a combination of starter and main dish or main dish and dessert, others have a starter, main dish and dessert of the day to choose from, seperately.
Beside all the restaurants, there are traiteurs. That's tiny shops which sell cooked food to take away. Mostily asian, but also traditional French or other dishes. Some have 2 or 3 tables but most are only counters with the offer and enough place to stand before the counter.
Bakeries are open from morning to 7pm mostly and most have take away dishes, pastries, salads, or combinations as a menu.
There are a lot of butcher shops and most will have some cooked dishes to take away.
There are cheese shops, selling hundreds of different cheeses, quite expensive but you'll never get such cheeses elsewhere.
Many bakeries sell cakes and chocolates and then there are shops which sell incredible chocolats, big brands or small shops who produce them locally.
If you are into organic food, just walk around, there are lots of organic food stores and markets - organic = bio.
Foods and shops differ from one part of the town to the other, but generally you can live very well without ever buying food in a supermarket. Not to forget the fruit stores, which are expensive but they have good quality and present it lovingly. You can buy one apple or 5 mushrooms, what I often do.
No to forget the markets: usually there are several during the week / week-end. Just look it up on Internet with your arrondissement / postal code and marché - where I live I could find a different one nearly every day at walking distance.
