The handbrakes are one of the more capricious of the systems on the CX.  This is one of the systems that is uniquely Citroen.  The main problem is that they are very likely to fall out of adjustment.

Several main causes of an adjustment that falls gets loose after about a week:

  1. Locking bolts insufficiently torqued.  I was surprised at how much torque was specified by the shop guide.  Use of a torque wrench is mandatory.
  2. Dirt and crap in the linkage.  The linkage gets filled with grease, dirt and brake dust.
  3. The inboard set screw is not pushed up against the caliper.
So,  a documentation of how I cleaned and reset one handbrake on the CX.
Remove the locknut and the retaining nut from the end of the cable at the inboard side of the caliper.  To ease removal, give the threaded end a good cleaning and douse the nuts with wd-40.  If they are really stuck, immobilize the end of the threaded shaft with some pliers and use a wrench to loosen the nut.  M7/ 11mm socket.
Pull the cable up and clear of the caliper linkage.
Loosen the ONE retaining bolt at the back of the caliper. 17mm socket. 
Put it in a bag and LABEL IT BEFORE MOVING ON TO THE OTHER RETAINING BOLT!!  I don't know if the bolts and eccentrics are interchangable, but it's easy enough to keep them separate and organised.
With the two retaining bolts removed, the linkage can be removed from the caliper.
Here are the places where dirt & brake dust accumulates and interferes with free movement of the linkage.
Items for cleaning the linkage.  I use engine degreaser and brake cleaner.  Please use NON-CHLORINATED brake cleaner.  There are good reasons why chlorinated brake cleaner is banned in several states.   Even non-chlorinated cleaner is hellishly toxic.   NITRILE gloves.  Do not use bare hands.  Latex will melt in about 5 seconds.

More information on the proper gloves to use.

and here also.

Eye protection is mandatory.  The brake cleaner is at a very high pressure, to dislodge the dirt & crap.  The fluid will splash back at you. 

I use a disposable aluminum baking pan for the small parts A wire brush was helpful to clean the eccentric and the retaining bolt.
Once the linkage is clean, it should get a good dose of grease.
Here, I'm using a feeler gauge to get some grease inside the moving parts.  Don't disassemble the linkage.  Just pack grease in there.  Rub some grease in the eccentric holes, and over the body.  The grease will protect the metal from corrosion.
That spring is under tension when it is in the linkage;  it's likely to pop out if not retained. Use a long screwdriver to hold it in place.
Before reassembly, you should check the thickness of the handbrake pads.  You know the tool that has the magnet on the end of a stick to retrieve dropped parts?  Perfect to remove the pads.  Otherwise you will waste an hour trying to get the pad out.  If any pad is less than 1mm in thickness, the entire set should be replaced.  Replace all the pads at once, not individually.
Now, the nightmare begins.