MARANELLO, Italy—Louis Camilleri’s appointment as Ferrari NV’s chief executive in July last year surprised many, including himself. Fifteen months on, his imprint on the Italian luxury sports car maker is becoming evident.

Mr. Camilleri is grappling with the rise of electric vehicles and the advance of autonomous-driving technology, while also seeking to return Ferrari’s storied Formula One racing team to success after a barren decade. On Monday, he laid out his plan to turn Ferrari into a luxury-goods brand that makes a range...