The costumes in Zeffirelli's film appear to be consistent with the clothing worn during the Elizabethan era ("Romeo and Juliet," IMDB). The costumes are also Italian Renaissance. Women wore corsets or bodices, as we see Juliet wearing in the balcony scene and men wore codpieces("Elizabethan Clothing," elizabethan-era.org.uk). So if we were to set the play at the time that Shakespeare wrote it, which was during the late Elizabethan period, then the costumes would be historically accurate.
However, there is a contradiction between Zeffirelli's costume choices and the true historical period that the play refers to. Prince Escalus actually represents Verona's Prince Bartolomeo I della Scala, who reigned for four years between 1301-1304, one hundred years before the Renaissance period, which was the Medieval period, and the codpiece was definitely absent from fashion in this period. During this time period, Prince Bartolomeo tried to put an end to the Verona feud between the Guelphs and the Ghibellines but failed ("Verona: The history," veronafor2.com).
The codpiece was most certainly not worn during the Medieval period. There is also a marked difference between the gowns in the film and the gowns of the Medieval period. Medieval gowns were often much more simple and fitted with belted waists ("Medieval Clothing," medieval-life.net). The gowns worn in the film are definitely Italian Renaissance.
Hence, the costumes in the Zeffirelli film certainly depict a historical conflict. They represent the Elizabethan era while the actual play refers to medieval times.