What Jack said. June is actually the worst month of the year for soccer in all western European countries; the seasons end in May, and preseason friendlies don't start until late July or into August -- and even then, are likely to be either overseas, for the top clubs, or against very local lower-level clubs, probably in their stadiums, which will be impossible to get into.

This season, for example, ends on May 22, and while next year's schedule won't be released until July, it will probably start on Saturday, August 27.

If you do change your schedule, Fiorentina is a top club and will certainly be playing next year (i.e., won't be relegated). To an Italian, a team fifteen miles away might as well be on the moon, but as an American you're not bound that way, so you could easily travel to Cesena, near Rimini on the coast, or Bologna to the north, both of whom are currently out of the drop zone, though Cesena by a single point. Siena, in Serie B, is also close, and they're likely to get promoted this season.

How easy is it to get tickets? I dunno. I'm seeing conflicting information. http://www.footballinitaly.com/travelplanner.html says it's pretty easy at various club-associated bars and other outlets, which your hotel should be able to help you with. But the site may be old; there are new very strict controls over who gets to go to the matches and in what part of the stadium -- there is absolutely no mingling allowed between supporters of different clubs. You will have to declare (and you should declare for Fiorentina, obviously).

Fiorentina's fans are notorious but unless you back into a flare or something you should be perfectly safe, especially if your kids are with you. Some Italian lunatic might teach them how to say something spectacularly offensive in Italian, though!

The easy way is to go through a broker, who will charge you an arm and a leg, but will get you a working ticket for sure. I'd try the hotel first.

The other option is to see what else is on at the stadium. Fiorentina's stadium is a top venue and Italian international matches will be played there. The European Championships are next year and qualifiers are being played now. In June? Italy's playing Estonia on the 3rd (subject to change) but the stadium isn't announced -- it could be Fiorentina, but it's unlikely. There are other events there, too, like concerts and even Rugby Union.

More info:

http://www.budgetairlinefootball.co.uk/636/35001.html

http://members.virtualtourist.com/m/75cf2/24e41/d/ (warning: popup hell)

http://en.violachannel.tv/ (official site, in English, sort of)