Cut the peaches into thin, bite-sized wedges, removing the pits. Place the peach slices into a large mixing bowl.
To prepare the melon, cut it in half lengthwise, removing the seeds. Cut each half again lengthwise, so the melon is in quarters. With a knife, slowly carve the outside skin off each melon quarter. Cut the wedges into a large, rustic dice and add the melon to the bowl with the peaches.
Crumble the cheese into the bowl. Add the mint, olive oil, vinegar, and honey and toss to combine. Taste for sweetness, adding more honey if desired. Salt to taste.