There seems to be only a reporter from French news agency AFP constantly following the proceedings, so there are sometimes reports in French media, mostly when something juicy happens, like when the defense wanted the trial to be thrown out of court because of alleged partiality of BEA experts (the court declared they wouldn't stop, but factor that in their deliberations) or when Continental presented a 3D animation (which they paid 800,000 $ for) depicting an accident version where the aircraft was on fire several hundred meters before reaching the location with the metal strip (based on witness testimonials not included in the accident investigation report).
Interesting: Continental defense strategy is to declare Concorde unfit to fly. Continental lawyer is quoted saying that Concorde should have been taken out of service 1979 after the first tire incidents.