Radomir Antic's side take on the French in their next outing in Belgrade in September.
The evening might have been more comfortable for Serbia had Nikola Zigic's sixth-minute header gone in instead of hitting the bar, but they struggled to find a way past the impressive home keeper Jakup Mikkelsen in a windy first half.
Jovanovic finally broke the deadlock two minutes before the break when, after his initial shot from the centre of the area was saved, the ball broke back to the Standard Liege striker and he slotted home the follow-up.
The visitors, without the injured Nemanja Vidic and suspended duo Dejan Stankovic and Bosko Jankovic, had a let-off ten minutes after the break when Suni Olsen's shot was only just off-target.
They made sure of the points in the 61st minute, though, as Borussia Dortmund defender Subotic headed home Nenad Milijas' cross.