Hewetson, a Briton, said fishermen from the French vessel, the Jean-Marie Christian VI, used the hook to pull his boat close to theirs, then "began beating us with sticks".
The environmental group said that Hewetson and other Greenpeace activists were trying to submerge part of the trawler's net to free the fish in a "non-violent" intervention when the clash occurred.
Greenpeace said several French tuna vessels surrounded the Greenpeace boats, threatening them with knives attached to long poles, and some of the fishermen also fired flare guns at a Greenpeace helicopter hovering overhead.
CNPMEM, the French fishing industry union, responded saying Greenpeace attacked the fishermen and tried to destroy the French boat's net.
Hubert Carre, its director-general, said it was not clear whether the sharp tool that caused the injury came from the fishing boat or a Greenpeace dinghy.
The union stressed that the French fishermen were acting legally and said all such boats are required to have an international observer aboard to verify that they are not underreporting their catch.
France's national fisheries body also backed the fishermen, saying they "were attacked by helmeted Greenpeace activists, equipped for and engaged in a violent operation - the destruction of a work tool."
The Federation of Maltese Aquaculture Producers criticised the Greenpeace activists, saying they had "sought confrontation, and got the confrontation they wanted".
Alexandre Faro, a Greenpeace lawyer, said he would be lodging a complaint for alleged wounding and assault with Paris prosecutors on Monday.
Industrial-scale fishing and harvesting has caused stocks of bluefin tuna to plunge by up to 80 per cent in the Mediterranean and eastern Atlantic, where they come to spawn in the warmer waters.
Many of the boats that fish in the Mediterranean carry net cages to contain the tuna, which are then towed offshore to be fattened and shipped in giant freezer ships to Japan, where they are a mainstay of sushi and sashimi.
Earlier this year the European Union and the US supported an international trade ban on tuna fished from these waters, but Japan lobbied successfully and the proposal was defeated.