to live and work in Germany without previously asking for a working visum you need a special kind of a residence permit in France, a long-term EU-wide residence permit. If I understood properly, it must be Carte de résident portant la mention "résident de longue durée-Communauté Européenne". You can ask for this in your French aliens department (service des entrngers). After many years with a refugee status it must be easy.
With this residence permit you can come to Germany visumfree for 90 days and ask for a German residence permit §38a Residence Act (Aufenthaltsgesetz). You must have a job offer which secures your living costs (the job agency must agree that you can do this job in Germany, it is normally not a problem for a qualified job if you would't earn under the usual amount for this kind of work in this area) Also you must have a medical insurance. If you don't have a job offer, you must have enough money, for example as property, to guarantee your living.