being from Nice, i think you can totally live here with 2500 euros, the average salary is around 1000 euros and people originally from Nice are forced to move out because the rents are getting too expensive
To rent a single bedroom, in a safe area, you need around 600 to 800 euros per month.
A coffee is 2 euros , a loaf of bread is 1,50 euros, a movie ticket is 10 euros, a meal is about 20/30 euros person in a normal restaurant.

I can see why you fell in love with Nice, being my hometown, i still find it beautiful, but living here can be "hell" , the traffic is horrible, things move slowly as people aren't really "workholics" here (don't forget it's a southern town!) and you may find it hard to deal with the lack of politeness from my fellow "niçois"
should you need more info, feel free to email me