Let's add that the few remaining spots left in Piazzale Michelangelo are also now PAID parking and there no longer is any free parking there.
In any case, if you are a DISABLED driver and have the EU disability card for your car, then you can park anywhere in the city for free, whether in the disabled spots or not. Just make sure your pass is visible. I would still be wary of not entering the ZTL area but in any case try to find parking closer than the piazzale where I do think there is 1 spot for disabled visitors.
The disabled spaces within a few of the parking structures managed by Firenze Parcheggi are actually outside of the parking structure itself (specifically, the lots at Piazza Ghiberti, Parterre and Porta al Prato) and you can also park there for free. The disabled spaces inside the other structures (such as at the SMN train station) are also free but you need to follow this procedure when you arrive at the parking entrance:
1. press the SOS button and wait for an operator to answer - expect majority of the operators to only speak Italian and be patient in trying to communicate you need someone who speaks English and waiting for them. Do NOT take a ticket, do not attempt to do this on the entrances marked TELEPASS - these are fast lanes for those with special machines inside the cars who don't need to pay every time they go in and out but receive a bill at home.
2. Give your car license plate, the country of origin where your pass was issued, number and expiration date of your disabled pass. If there are disabled spaces free within the parking, the operator will have the machine at the gate issue a special ticket you will use to enter and to exit the parking structure. The pass will say how long it is valid for, it should be valid for more than a day.
Don't take a normal ticket or go through the Telepass gate to enter the parking structures, as then you'll be required to pay for the time you parked.
Hope this extra info helps!