Normally, all clothing stores, supermarkets and others: bookstores, sports supplies, gift stores, will accept debit and credit cards. However, magazine and newstands, tabaccherie (for purchase of postage stamps) do not usually accept cards.
Suggestion: prior to making a purchase, ask the clerk what forms of payment are accepted. If the store does not accept cards, you will need to find a bancomat (debit card withdrawal machine) and withdraw the needed cash.
IMPORTANT: be sure to obtain a receipt for ANY and ALL purchases, for any forms of payment used.