Nice has a busy fish market every morning except Monday in Place Saint-François, in the old town, open every morning except Mondays.
It starts at 06:00 and runs all morning. There is an exceptional choice and prices are competitive. You might need to battle with the seagulls for the fish though as they are very persistent!
Despite being on the sea, the geology of the coastline actually means that there are very few fish in the sea in front of Nice. They are, however, caught from neighbouring coastlines and brought fresh to the markets of Nice so you can be assured they are fresh and local in that respect.