The Christchurch Call is set to continue as a charity, rather than as part of the government.
The initiative, established by former prime minister Dame Jacinda Ardern, aims to stop violent extremism online.
It was set up in 2019 as part of the Department of Prime Minister and Cabinet, but it will now become a separate entity with charitable status, called the Christchurch Call Foundation.
The change is the result of the November 2023 Christchurch Call Leaders' Summit.
In a statement, Macron said the Christchurch Call was committed to tackling online extremism.
"Our commitment to this promise remains firm and I am confident that this new stage of the call provides a solid basis for the future of this initiative and the new challenges we now have to tackle, including AI-generated content."
Dame Jacinda will continue her work on the initiative, in the new role of patron of the call.
She marked the change with a statement, posted on Instagram.
"When I left the role of PM, one of the things I wanted to keep working on was the Christchurch Call to Action - a community of leaders, tech companies and civil society committed to addressing violent extremism and terrorism online. It has always been a multi stakeholder group, but the day to day running of the organisation has primarily been funded by the New Zealand government," Dame Jacinda wrote on the Instagram post.
"The NZ government of the day continues to support the mission of the Christchurch Call, which began after our Muslim community experienced a terrorist attack on 15 March - but to be a truly multi stakeholder body the secretariat will move out of the Department of Prime Minister and Cabinet, and instead become a separate legal entity with charitable status.
"I have advised the prime minister that it makes sense for my role to change, and at the same time the new organisation is stood up I will no longer be special envoy to the prime minister but rather patron of the organisation as a whole."
In a statement, the Federation of Islamic Associations of New Zealand (FIANZ) thanked Luxon for his ongoing support to the project, saying New Zealand played an important part in efforts to eliminate online extremism.
"The call is now a recognised major international body and credit must be given to officials of NZ and France who have managed the process till now," Abdur Razzaq, chairperson of the FIANZ royal commission follow-up, said.
He said it was appropriate for Dame Jacinda to carry on in her new role with the initiative.
Luxon thanked Dame Jacinda for her "advocacy and leadership of the Christchurch Call, which has curtailed violent extremism online".
"I wish her and the Christchurch Call well as they evolve in the next phase of their development," he said.
The move to a charity will mean the Christchurch Call no longer receives public funding.
The statement said the Christchurch Call Foundation had already received pledges from members of the Call Community and philanthropic donors.