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Why would the NTSB have to be involved?
Simply because, depending on the final results, certification of the aircraft to be flown by U.S. carriers might be affected.
There is no reason for the NTSB to be involved unless one of the parties (France, Germany or New Zealand) request their assistance for some reason.
The investigative process is none of their business and they have no remit.
The report that eventually will be circulated will be taken on board by the myriad certification authorities around the world (in the USA the FAA, NOT the NTSB) and each will decide on how it will act - most likely in concert with the others.