Regardless of if Germany has Paris, France or not, if Italy takes S. France, all they get is S. France and collect income as per any other territory conquered during the Conduct Combat Phase of the game. They never get treasury IPC for taking a territory, unless they take a capitol (Calcutta, India; Sydney, Australia; Washington DC, USA; London, England; Moscow, Russia; Berlin, Germany; Rome, Italy).
Taking a capitol is an exception to the rules, it is not a standard rule for taking any territory.