Does anybody know if I can do my JAA FI(R) in France, or do I have to take a different Flight Instructor's course?
Yes, you can do your JAA FI(R) in France. I have a French friend with CAA CPL, who did French FI, and who is now instructing in France.
I would respectfully suggest though, that unless your French is very good, and that you have fluent "cockpit" French, you will not be able to compete the FI course, as it will all be done in French.
You would really need a French FI to have much chance of getting work in France, though I have read on here of an English lady who got permission to instruct in English in France with her UK FI.
Also, what are the chances of getting a job as an instructor in France,
That depends if you want to get paid or not. Many instructors at aeroclubs are benevoles (voluntary) (Don't let Flintstone see that or he will have another fit!). To get a paid instructing job, you mostly need to work at an FTO.
I think that there is a need for English mother tongue instructors in France at FTOs, especially with the new language requirements. Certainly at the FTO where I did my training, there were a number of pilots who would have preferred instruction in English, but none of the French instructors really had the necessary level to teach in English to the same standard that they could teach in French.
I suspect that the DGAC will not relent on their protectionism to French pilots in the near future however. Bear in mind that they do not even accept a CAA FRTOL as giving you the right to speak English on the radio.