Depending where your Florence flight lands at A gates, it may take a good 10 ten minutes to find an elevator to Z gates. Then, you have to go through customs. The passport line was pretty short for me last Friday. At your UA flight gate, you will need to get a sticker on your passport before boarding.
So, if your connection flight from Florence is on time and the plane is not parking at a remote site, you should be able to make it in 60 min. Good luck.