Your question: Florence is built on both sides of the Arno River.
or
Florence was built on both sides of the Arno River.
You are asking which sentence is correct.The builing process of Florence Was finished long time ago. So, you can't use 'is' in the sentence. However, 'was built' implys that florence was buit by someone else. Look at the following sentences:
John ordered daisy to go to the marked.
Daisy was ordered to go to the market.
The first sentence is active voice statement. The second sentence is passive. In passive voice sentence, we can guess that daisy was ordered by someone else to go to the market. Your Passive voice is also has been used in this sense.
I hope it helps.