Parisians Don't Buy Brooms
Shopping for clothes and shoes is easy enough because those stores are everywhere, but coming to Paris when you're used to Bed, Bath and Beyond, Homegoods or Target is a real pain. It's hard enough getting used to new clothes stores (because you're not going to find a lot of your favorite American brands), finding out where to buy sheets, towels and duvets is a little bit harder.
Of course you have IKEA, but they're all located outside of Paris, and if you don't feel like taking the metro, much less the RER, then you'll have to suck it up and find a few of these places.
I'm Rive Droit so I can't give a lot of advice on what's in south Paris but so far if you live near Ledru Rollin consider yourself lucky. Not only does Faubourg Saint Antoine (towards Bastille) have the best mile of shops, you also have stores like Casa (mostly outdoor), HEMA and giant Monoprix (French call those hypermarches).
If you need dishes and kitchen stuff, unfortunately you won't find a Williams Sonoma, but there are a few little unassuming home stores. I never remember the names but if you walk Saint Antoine from Bastille towards Saint Paul, there's a nice little place that sells cute bowls and glasses and things. Across the street you have Confordeco. And for a cheap little linen store, from Chateaudun towards Saint Lazare (I want to say metro Trinite...), there's a place that sells duvets, towels, robes, etc. Unfortunately stuff like towels, while being super cheap in the US ($6 for Ralph Lauren from Ross anyone?), they're a bit more expensive here. You're going to spend anywhere from 30-40€ for one normal sized towel (but at Hema a bath sheet is only 13€, bargain!).
If you're into getting your pillows, carpets, sheets, and clic clac all in one place, try stores like Habitat, Conforama, and if you don't mind a department store, BHV. It's going to be more expensive, but I guess it beats going to many different places. If you live in the 13th or the 18th, try Tati (cheapest).
If you're interested in an Anthropolgie aesthetic and want something a little more fashionable, try Madura or Zara Home. Yes, for some reason Zara has a home store. I didn't even know such a thing existed before I walked down Rivoli one day and saw it.
If for some reason you need a Home Depot/Lowe's, Castorama is located at Place de Clichy, near Montmartre cemetery. For a Best Buy type store look for Darty or FNAC.
As for the hyper Monoprixs, so far the ones I know of are Ledru Rollin (11th), Saint Augustin (8th), there's one on Sebastopol near Chatelet (4th), the 7th near Rue de Bac or Solferino? and the 15th on Commerce. Carrefour in the 13th at Place d'Italie (inside the mall) is also a hypermarket. It's also the biggest grocery store I've ever been in (in Paris).
The best time to buy products is definitely during Soldes. Things get relatively cheaper during this time of year. You can even pick up fancy sheets from Yves Delorme and Deschamps for 40% off. BHV also has a good home sale during this time. And o definitely clean up pretty well at Monoprix. But be warned if you’re looking for some really cheap prices, it’s not likely to happen. I have never really seen nice stuff at more than 50% off. I like to get a good 60% or more to really consider it a bargain, and so far by dernier marque (last marks) anything at 70% off isn’t worth it or nothing is left.
Updated- to say Zara Home during the summer 2019 soldes gave me a lot of bargains. I think it was because the Zara I frequented is less popular than other locations, but I bought plenty of linens for 20€ or less. I can’t find a place that does a really good sale on pillows and duvets (Habitat is where I got mine), but Zara Home really pulled through.