French gendarmes check vehicles in Ducos, on the French Caribbean island of Martinique. AFP

Two French ministers were due to travel to the Caribbean as concern grows over spiralling Covid-19 infections as France's overseas territory of Martinique will enter a tougher lockdown for three weeks from Tuesday to tackle a coronavirus outbreak on the West Indian island.

Administrative authorities in Martinique also advised tourists to leave as the island had already imposed an evening curfew, set to start from 7pm, that will shutter shops selling items that are not essential, such as food, as well as closing beaches and clamping down on people's movements.

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Last weekend, French health minister Olivier Veran appealed for volunteer doctors and nurses to travel to the overseas territories of Guadeloupe and Martinique as a wave of COVID infections overwhelms hospitals on the two Caribbean islands.

Guadeloupe and France's island of La Reunion in the Indian Ocean have also imposed curbs against the virus.

Local residents queue up to take a Covid-19 test at a laboratory in Fort-de-France, Martinique. AFP

There are now 1,200 cases per 100,000 inhabitants on Martinique, while only 22 percent of the population have received even a first dose of the vaccination.

"These rules are strict and they will be lifted as soon as the health situation allows it," the top official of Martinique, Stanislas Cazelles told reporters in its main city of Fort-de-France.

French Overseas Territories Minister Sebastien Lecornu and Health Minister Olivier Veran are both expected in the Caribbean later Tuesday for visits to Martinique and neighbouring Guadeloupe, which is also in a lockdown albeit less strict than that on Martinique.

Veran had earlier this week made a video plea on social media for medical workers in mainland France to show "national solidarity" and volunteer to help the stretched medical teams on the islands. Some 240 volunteers are now due to leave on Tuesday.

Meanwhile, the US State Department has advised Americans to avoid all travel to France over rising coronavirus cases in the country.

France is battling a fourth wave of the virus even though Covid-19 hospitalizations are still way off previous highs.

The State Department issued a "Level 4: Do Not Travel" advisory for France on Monday, based on a parallel warning from the US Centers for Disease Control, the country's top medical body.

"If you must travel to France, make sure you are fully vaccinated before travel," the CDC said.