Set aside ¼ of the chopped onion in a medium bowl for the salsa.
Heat the olive oil over medium heat in a large sauté pan. Add the remaining ¾ of the chopped onion and ⅛ teaspoon salt. Sauté 3-5 minutes, stirring occasionally, until the onions are softened.
Add the turkey, garlic, cumin, and ⅛ teaspoon salt. Cook the turkey, stirring occasionally until browned and cooked through, about 8 minutes.
Meanwhile, make the salsa by combining the peaches, lime juice, onion, basil, jalapeño (if using), and salt in a medium bowl, stirring to combine.
Make the tacos by filling each tortilla with cooked turkey and topping with peach salsa.