Lyman;
I do not know who mandated the search be controlled by BEA, the Court?
ICAO Convention Annex 13 provides that mandate to the State of registration for an aircraft lost in International waters. The BEA is the designated responsible entity in French law.
Any Search and Rescue response is that of the State in who's SAR AREA the accident occurred; in this case Brazil. The BEA was able to consult with Maritime experts and put together an initial TPL search for the ULBs without impinging on the Brazilian SAR efforts - be they misplaced or not. But in like vein, the BEA was able to enlist the naval and air resources of the French state to work
with the Brazilian Military.
The BEA was always ultimately the legal custodian of any bodies or items recovered during the SAR phase or later. Not having the resources in the initial stages to handle/store recovered bodies, that task was left to the Brazilians. Once the Brazilians declared the SAR operation to be complete, the BEA was left unfettered to proceed at its leisure to instigate its own Search and Recovery plan. One small complication was the criminal investigation proceedings commenced in France, which gave the court the power to place evidence under seal.