Place cucumbers in a medium bowl and season with salt. Spoon half of vinaigrette over and toss gently to coat.
Place peaches in a serving bowl or on a platter and season with salt. Spoon remaining vinaigrette over and toss gently with your hands to coat.
Add cucumbers to peaches; toss gently again just to combine. Add feta; season with salt and pepper. Top salad with basil and mint and squeeze lemon over.