Rapid search on internet with
noleggio apparecchiature fotografiche Firenze I extracted a couple of suitable shops, but I don't know them so I cannot give any reference.
Ottica Bongi, belonging to the Photop nework, via por Santa Maria 82/84 (1 minute walk from Ponte Vecchio, historical centre)
http://www.photop.it/negozi-di-fotografia/item/bongi.html
http://www.estron.it/ in Via Siena, 37/2 50142 Firenze
(1 hour walk from Ponte Vecchio according to Google Maps)
As you can see, the first is straight in the centre of the historical centre, easy to find. The second needs a bit of walking, and is given as an "emergency" in case the first one remained without tripod for rent.
If you mail them they might perhaps reserve a tripod for you on the day you arrive, possibly with a down payment. That would make things easier.