Cut the watermelon into cubes.
Cut the peaches into small pieces.
Arrange the watermelon, peaches, cucumber, and red onion in a large serving bowl or platter.
Scatter the crumbled feta, fresh basil, and toasted nuts (if using) over the top.
In a small bowl, whisk together the olive oil, lemon juice, vinegar, honey, Dijon mustard, salt, and pepper until well combined.
Drizzle the dressing over the salad just before serving.
Toss gently to combine, being careful not to break up the watermelon or feta too much.
Serve immediately while everything is fresh and chilled.