Tried booking a restaurant in Florence only to have it cancelled.

It sounds like you encountered a computer glitch. Yes, you can make reservations for meals ahead of your arrival, It is a good idea and necessary over the holidays.
Try again or choose another restaurant. We have
been in London andd Rome over the holidays and many places are closed. But you can find some that are open. Keep trying! Or contact your hotel’s concierge or front desk for assistance in making reservations for you.

I haven’t left for Italy yet so I can’t call the hotel for this. Is there no other way to book aside from online? My phone plan doesn’t cover Europe so I just go without booking? I was really trying to get into a few places that are supposed to be good.

Well, you could also email the restaurant. Or even I booked my favorite restaurant in Florence via email. You could also email your hotel to ask for their advice.

I had to call SNCF, the French train company, a few weeks ago. I actually bought a batch of 100 minutes from Skype that was able to call French landlines and cell phones for $2.30. I called them via Skype and it worked fine. Now I am trying to figure out if I need to call France for anything else, as I have 93 more minutes to use this month! haha

This is strange and rare. Was there any additional verbiage that came with the cancellation? If you go back in, do the dates and time still show up? The one time this happened to us was when a restaurant failed to update their online system and we booked for a date when it was actually closed for a week. Sure enough when we went back in the whole week was greyed out. Maybe that's what happened here? But to your larger question, there shouldn't (generally) be problems booking in advance, either from the U.S. or while over there.

You can reserve a lot of restaurants through google maps and TripAdvisor.

Email your hotel and ask them to make the reservation on your behalf.