I believe you are referring to Calcio Fiorentino, or Calcio Storico. Happens in June in the Piazza di Santa Croce with the final always being played on the 24th June, which coincides with the day of the city, the feast of San Giovanni, the city’s patron saint.
Short description: gladiators from the 4 historic districts of Florence playing football. It’s pretty brutal and violent. It’s the Renaissance-era version of ‘Fight Club’ (Florence’s Fight Club).
Calcio fiorentino (also known as calcio storico “historic football”) is an early form of football that originated in 16th-century Italy. Once widely played, the sport is thought to have started in the Piazza Santa Croce in Florence. There it became known as the giuoco del calcio fiorentino (“Florentine kick game”) or simply calcio; which is now also the name for association football in the Italian language.
This 5 minute video will give you the gist of it:
Dates for the semi-finals of Calcio Storico 2018 are not known yet. They’re drawn around Easter time, but usually one week earlier than the final which is on the 24th June.
Official site: http://www.calciostoricofiorentino.it/