Those in the know aka locals head to the Liberation market located one tram stop north of the main train station [Nice Ville] in the General de Gaulle Square
In addition to the outside stalls with produce and fish there is a small indoor market which is full of meats, fish [best selection in Nice], cheeses, honey, olive oil etc.
Hours are 6am to 12:20p every day except Monday and prices are less than Cours Saleya plus you get the real local experience. A must visit and fewer tourists!
Two other markets worth a visit are the Antibes market [Tuesday to Sunday] and the Friday morning market across the border in Ventimiglia.
Le Marché Provençal is the main attraction. Open daily from 6 am to 1pm daily [except Mondays in winter]. Located in Cours Masséna, this covered market offers a wonderful selection of local produce. Good to visit in combination with the Picasso museum. As for Cours Saleya market, sit in one of the any cafes and enjoy the food and people watch
The Friday morning trip to Ventimiglia [by train] has three attractions. First: the best canolis ever at a little bakery [Prodotti Motta} just down from the station at#1 Via della Stazione, towards the sea – you have to get there early because they are sold out by 10 am.. Second: a little further down the road is a fabulous indoor market [Mercato dei Fiori] – great for olive oil, and Italian meats. Lastly the Friday market along the sea front which is considered the largest in Italy. Here you will find a wide choice of items, including clothing, leather items, shoes, cashmere and more. Prices are subject to discussion and you must be aware that some products can be fakes, particularly high fashion items – cheap usually = fake!