The greatest usual cycling race here is the stage race Paris - Nice, every year in March. If you like cycling and want to compare yourself with the champions, read this article.
55km away from Nice is San Remo. An other famous race, Milano - San Remo (almost 300km) ends there. It happens in March, one week after Paris Nice. In 2015, it'll be back on its historical finish line, Via Roma.
The Tour de France came in Nice for the last time in 2013. But the Great departure in 2020 will take place in Nice, for 2 stages.