For pickled peaches, in a small bowl whisk together vinegar, honey, fennel seeds, and salt. Place peaches in a large resealable plastic bag set in a shallow dish; pour marinade over peaches. Seal bag; rotate to coat. Let stand at least 20 minutes.
Meanwhile, preheat grill to medium. For Arugula Mayo, in a small bowl combine chopped arugula and basil and the mayonnaise; set aside.
Grill hot dogs on the rack of covered charcoal or gas grill, directly over medium heat, for 5 to 7 minutes, turning occasionally. On each bun, spread with 1 Tbsp. Arugula Mayo. Layer bacon and hot dog. With slotted spoon, scoop some peaches on dogs. Top with arugula, if desired. Serve with remaining peaches. Cover and refrigerate Arugula Mayo up to 3 days. Refrigerate peaches up to 1 day. Makes 8 servings.