I have never done a parachute but I did have to make a sail that was puffed up in the wind sort of like the parachute would be after the landing when it catches the wind. What I did was to use wire as the rigging and it shaped the general curve, then before I put the sail up I diluted some white glue and painted it on one side of the material and put it on a form I made from foam and paper. When it was done the white glue was stiff enough to give it support and there was a definite curve to the sail that would have sagged if I had only used the wire or just let it hang.
The only other thing I can tell you is to use the glue on the side of the parachute that is the least visible, the glue leaves a visible shine, although the sail I was doing had no color and a parachute can be painted depending on the scene you are creating.