France is willing to discuss autonomy for the French Caribbean territory of Guadeloupe if it is in the interests of the people who live there, government minister Sebastien Lecornu said.

Guadeloupe and the nearby French island of Martinique have seen several days of protests against COVID-19 measures that have spilled over into violence.

Lecornu, the minister for France's overseas territories, said in a YouTube video issued late on Friday that certain elected officials in Guadeloupe had raised the question of autonomy, changing its status as an overseas region.

"The government is ready to talk about this. There are no bad debates, as long as those debates serve to resolve the real everyday problems of people in Guadeloupe," he said.

That was one of a series of initiatives he said the government in Paris would be taking in Guadeloupe, including improving healthcare, infrastructure projects and a scheme to create jobs for young people.

The French government this week announced that it would be postponing a requirement that public sector workers in Guadeloupe and Martinique get a COVID-19 vaccination.

That had sparked protests, fanning long-standing grievances over living standards and the relationship with Paris.

In Guadeloupe, there is a historic mistrust of the French government's handling of health crises after many people were exposed to toxic pesticides used in banana plantations in the 1970s.