Parking in Florence is really expensive and can be a real challenge.
The city center is a limited traffic area (ZTL) and you cannot drive in without special permits or without getting a fine
If you are staying in an hotel or other accommodation in the historical center within the ZTL area, ask the owners for parking lots or garages in the area near the apartment. They generally have special agreements with private garages and provide you with better fares.
If you are staying outside the ZTL area but still in Florence city, you can park along the streets in blue lines which still are paid parking spaces and you have to pay attention to weekly street cleaning. You can ask for more information about parking in a specific area at your accommodation.
Outside the city center there are a few free parking lots. You may have a look at the map of parking lots in Florence. The blue P areas are on payment, the green ones are the free ones.
The free parking lots we mentioned in the article are generally safe and you can park there as long as you wish.
I personally suggest you find an apartment or another accommodation in Florence surroundings so that you can park your car there for free and go to Florence by bus. Bus tickets won't cost you as much as a daily parking rate in Florence. In addition you can escape the heat in Florence which can be terrible in these months. It is quite warm already.
I hope my suggestions help you out. Don't hesitate to come back with other questions