Using a mandoline or a sharp knife, cut the green and red cabbage very thin.
Add the green cabbage, red cabbage, carrot, onion, and jalapeño to a large bowl.
In a small bowl, whisk the apple cider vinegar, olive oil, peach jam, Dijon mustard, cumin, salt, and pepper until the jam fully dissolves and the dressing looks smooth.
Pour the dressing over the cabbage mixture and toss well.
Slice the peaches.
Gently fold in the peaches and cilantro just before serving so the slices stay intact, and serve the coleslaw.