If the outer handle is just flapping then the hinge pin is probably broken. If there is some feel to it then the actuating rod has likely slipped or come out. The inner handle will not operate if the child locks are on, but unfortunately this can only be accessed with the door open.
The panel can be removed with the door closed, although it is a bit fiddly. I have a 2000 Synergie, which has three screws, one each at the bottom trim, fore and aft and the third is visible when the ash tray is removed. Otherwise the trim is secured with the usual pop fasteners. I found it easier with the adjacent rear seat removed entirely to allow access to the lower screws. You will also have to remove the locking button at the top of the trim, the plastic trim around the inner door handle and the window switch if electrical. The connecting block for the window switch can be reached when the trim is part removed. Hope this helps.