There is no JAA CFI rating its a FI rating. As you already have a FAA CFI then depending on your experience, you may get some credit towards the JAA FI Course. If you have over 500 hours flight time of which 200 are as an instructor, the training may be reduced on the recommendation of an FIC instructor to the CAA, to a minimum of 15 hours flight training and 30 hours ground training. If you don't have the hours you will have to do the full FI Course 30 hors flying and 125 hours theory.
You can not be paid for instructing without a JAA CPL.