How old is the car and how long have you owned it? Do you know any of it's history at all? FIAT recommend changing it at 5 years or 75,000 miles - whichever comes first. The 500 - I'm assuming it's got a belt type engine and isn't a twin air? - will have the 69hp VVT engine so is an interference type which means if the belt jumps some teeth or comes off the pulleys or breaks then serious and expensive valve/cylinder head damage is very likely so, if you can't be sure the belt is within the recommended interval I'd just do it - complete with tensioner and water pump as they are directly part of that drive system.
Even if you can get a good look at the belt my experience is that cam belts tend to look absolutely fine almost right up until they fail so a visual inspection is not a very reliable way to ensure a belt might be ok to go on for, say, the next two or three years. Also, often it's not the belt itself which fails but more likely the water pump bearings failing and letting the belt jump the teeth or come right off the pulleys altogether.