Have you read my article on weddings in Florence?
The link to the marriage page on the city website has info in English!
I want to make clear that dealing with Palazzo Vecchio directly isn't easy!
The main problem is they don't have staff that speaks English -- last year I called for someone who posted on our forum here and asked for help, I called to ask about English speaking staff and they honestly told me they had one person who knows a little English but obviously is not always on hand.
The easiest solution is to use email -- but if you have difficulty getting replies from them, then the only work around is to get someone local, like a wedding planner, who can help you deal with this aspect (and only this aspect if that is all you want help with).