A ground plane on an FFC does two things that provides shielding and a path for return currents. 

The shielding helps because it creates capacitance directly adjacent to the trace so electric fields have less of a chance to radiate and want to return to the source which means you're more likely to have a better chance of passing FCC.

With high speed signals you must have a ground plane directly underneath the trace or adjacent to the trace to carry return currents and minimize inductance otherwise then inductance is too great and it affects the rise time of the signal.

Some molex cables have the option of EMI shielding instead of a ground plane. What we ended up doing is doing a custom FPC with a ground plane and we had much better results on FCC tests. (You can make your own FPC that fits into molex if you follow the dimensions of their cable)