There are a few ways that cities can grow to become how we see them today. Some cities start out as a small collection of buildings and new buildings are added and spread out from the original area. Some cities are built completely from scratch with very detailed plans of exactly what is going to go where and how the streets will look. Most major cities in the United States follow this second approach. Nice is a little different in that it was built and rebuilt over and over again depending on who was the official ruler. Most of the city you see today was built under the Kingdom of Sardinia (just like the fish!) or by the French during what was called the Belle Époque (Bell Ay-pock). This was the period of French and European history between 1880 and 1914.
The Kingdom of Sardinia existed before a bunch of kingdoms came together to make up what is modern Italy. Nice was supposed to be a major city of that newly-created country and was included in plans to bring the kingdoms together. This is why a lot of Nice, especially the "old town", feels more like you are in Italy than in France. The plants, the colorful bricks, and buildings, and much of the architecture in "Old Nice" has a very strong Italian feel because of it's origins.