Vieux-Nice (or Old Town) is the formerly walled medieval part of Nice.
Unfortunately, I don't know exactly when its streets were laid out. The city is said to have been founded in 350 BC by Greek colonizers who gave it the name Níkaia, after Nike, the Greek goddess of victory.
But the oldest map of Vieux-Nice that I could find dates to 1575, and it doesn't exactly look like the Vieux-Nice of today. So it's hard to say. Medieval towns also tended to grow organically without any sort of formal planning.
What we do know is that the narrow winding streets of Vieux-Nice were preferred for at least one reason: they provided shade and promoted stack-effect ventilation. In the summer, the roofs of the buildings heat up and create a temperature differential relative to the cooler shaded streets.
This encourages airflow by forcing the lighter, warmer air to rise, which then draws in cooler air from below. Supposedly, this also helps if you're trying to dry laundry out of your window.
Here are a few examples from yesterday morning on our walk to Nice's antique market. This is the narrowest street I could find without trying very hard. And yes, it's a street with a bona fide street sign.



