"Courthouse" would be "palais de justice". "Tribunal" refers to the system, concept, or jurisdiction, not the physical building. There's a similar difference in English. "He needs to appear in court" is said rather than "in/at the courthouse". The implications are different as well. "He works for the court" could mean a judge or lawyer, but not a janitor. "He works for the courthouse", could certainly mean a janitor but less likely a judge.
Larousse and WordReference both seem to feel that un tribunal could be either a court or a courthouse.
"He works at the courthouse" is now accepted, btw.