I'm familiar with Sainsburys, Waitrose, Tesco in the UK, and with small shops in London in particular. I'm interested in something similar to visit on day one in Paris to pick up a few things and looking for store names so I can locate near our neighborhood. Yes we will visit the more traditional spots for food shopping while we are there, but after a transatlantic flight with two kids, some quick and productive food shopping in the way of a Sainsburys, etc. to stock up on snacks will be in order. Thanks!
Carrefour and Monoprix are the everywhere chains (and there are a lot of independents as you would expect). I love going to European grocers as beer wine there that is normally a pricey import only available in specialty store stateside is inexpensive at chain stores. Try to bring your own bag (called a sac) , it is not assumed that you need or want one like here in America.
Or go without any bags! I love to buy all the local chain branded bags while I’m shopping there. They make awesome and cheap souvenirs. I use them on the trip and then pack them since they are so small and weigh nothing and when I’m visiting friends and bringing food or something I deliver it in the bag and leave it with them. They love it and reuse them all the time. They can also double as emergency carry on bags if you need it. One of my decade old Carrefour bags has been passed around so often it’s travelled farther than me.
Monoprix shopping bags make great light, packable €1 gifts to take home (many, many designs) It's usually our first stop in Paris -- snacks, candy, paté, cheese ...
There is always, of course, the "corner shop" for emergency items (wine!) and snack-y stuff. And the Ed Supermarket stores are less expensive than than the other big supermarkets, if you come across one.
Just find your address on Google maps and then use "Nearby". Always worked for me.
If you’re near Le Bon Marche its Grand Epicerie is fantastic. Gorgeous grocery store that’s an experience in and of itself. https://www.lagrandeepicerie.com/en/index
Franprix is another local neighborhood place.
La Grande Épicerie is a fabulous space but very expensive. That's logical since it's part of the Bon Marché.
My apartment landlord had a notice of what was close, but if planning ahead, I use the Google Maps 'nearby' function.
Monoprix has cheap carry bags that have double handles -- long loops of cloth tape and short handles that have a plastic tube over the tape and thus are easy on the hands when carrying heavy groceries a ways. We always bring several back each trip as we do most of our grocery shopping on foot in Chicago and these bags are the most comfortable we have found. They are made of recycled plastic and so wear out, but they are fairly durable and very comfortable to carry.
There are small outposts of Monoprix, small Franprix and Carrefour stores etc all over. Very large Monoprix supermarkets are here and there and excellent for stocking up the apartment. And in shopping centers there are usually large Carrefour super markets e.g. there is one at Gallieni end of the 3 line and one at Italie 2 at Place Italie. Of course if you are lucky there will be a fish monger, a couple of butcher shops and several bakeries near your lodging. Bakeries in an area cooperate so that one is always open Sunday morning and their closing days vary so there is always a place to get the morning bread.