According to the Trenitalia website, there is luggage storage at the Assisi station although I've never used or seen it. I think the first thing you need to do is figure out when this office is open (days of the week, time of day). Perhaps someone else here (kybourbon? GAC?) can decipher the Trenitalia website because I couldn't find this information.

Once you know about the luggage storage, you can check the train timetables to decide how early you can leave Florence and how late you can leave Assisi. Don't forget to factor in the time needed to ride the shuttle bus between the train station and the center of town. You won't be required to spend the night in Assisi, but you will spend several hours on the train that day.

You can check train schedules here:

http://www.fsitaliane.com/homepage_en.html

Well, according to a poster on this site, the office was closed in September 2011.

http://www.tripadvisor.co.uk/ShowTopic-g187905-i1049-k4783089-Luggage_storage_in_Assisi-Assisi_Province_of_Perugia_Umbria.html

... and I'm not finding any more recent comments on the issue of luggage storage at Assisi.

If you're staying at a hotel in either Florence or Rome, you might send emails, tell them your plan and ask if they can help with up-to-date information.