Giuoco del calcio Fiorentino

That is the name of the above sport played during medievial times.

The modern version of this sport has the following teams vying for top honors:

Santa Croce / azzurri

Santa Maria Novella / rossi

Santo Spirito / bianchi

San Giovanni / verdi

If fascists are to be believed, this is a precursor to a modern day sport which was “re-invented” later in another country. Which sport?