In the letter, the Mao Mana Foundation asked for clarification after the French High Commission reacted to the incident by saying no foreign ship was engaged in fishing activities in French Polynesia's waters.
French Polynesia was the world's largest shark sanctuary and by law it was forbidden to possess or transport protected species, be they dead or alive.
Last month, the Chinese ship Shen Gang Shun 1 ran aground on the reef of Arutua atoll and as salvage operations began, the mayor of Arutua and other fishermen discovered in its hold a number of frozen sharks stitched up with cut-off fins inside them.
The vice-president Teva Rohfritsch issued a statement a day after the discovery was reported in the local media, saying there had been no poaching in French Polynesian waters.
The government said the Shen Gang Shun 1 had been repaired and restocked in Papeete in mid-March and left with 15 tonnes of frozen fish on board along with 26 tonnes of bait.
The Mao Moana Foundation now publicly raised several questions.
It wanted to know what the consequence was of transporting a protected species through French waters.
It also asked whether the government maintained its position that there was nothing illegal with the activities of the Chinese vessel in question.
Further, it wants to know what the policy was for exports from the port of Papeete and who was in charge of inspections.
The Mao Moana Foundation said as the government pretended to be a leader in the protection of marine resources it should be easy to answer these questions quickly.
Earlier, the environmental umbrella organisation Te Ora Naho also raised the incident, pointing out that anyone found guilty of breaching the law risked a prison sentence of up to two years and a fine of up to $US160,000.
Te Ora Naho also questioned how it could happen that after the vessel was inspected it was allowed to leave with frozen sharks in its hold.
It said it may lodge a formal complaint, which would trigger an investigation.
Papeete, which is about 400 kilometres southwest of Arutua, is a key transshipment port for the Chinese fishing fleet in the southeast Pacific.
Photo: Te Ora Naho FB caption: Shark bodies stitched up with cut-off fins inside them