Radar echoes had picked up several objects about 1,430 miles from Perth, a statement added.
It is the third possible sighting in the area off western Australia that has become the focus of the search effort.
Malaysia Airlines flight MH370 disappeared on March 8 while en route from Kuala Lumpur to Beijing, with 239 people on board.
Malaysian officials believe the plane was deliberately taken off course.
Based on information received from a satellite, the search has been in two distinct corridors – one stretching to the north-west of the last known location in the Malacca Straits and one to the south-west.
However, none of the countries on the northern corridor have reported any radar contact, and the satellite images of possible debris in the south Indian Ocean have concentrated the search there.
On Sunday, a statement published on the Malaysian ministry of transport’s Facebook page said: “This morning, Malaysia received new satellite images from the French authorities showing potential objects in the vicinity of the southern corridor.
“Malaysia immediately relayed these images to the Australian rescue co-ordination centre.”
An unnamed Malaysian official told the Associated Press that the new satellite image was taken on Friday, and that one of the potential objects was estimated to be about the same size as one spotted by a Chinese satellite that appeared to be 72ft by 13m 43ft.
The possible debris was located about 575 miles north of where the objects reported by China and Australia over the past week, the official added.
A French foreign ministry statement said the objects were about 1,437 miles from Perth, but did not give a direction or say when the discovery was made.
It also clarified that the French authorities had passed on data in the form of “satellite-generated radar echoes” rather than images. Radar works by sending out radio waves or microwaves and listening for echoes that bounce back.
“France has decided to mobilize complementary satellite means to continue the search in the identified zone,” the ministry statement added.
The Australian Maritime Safety Authority (AMSA) subsequently announced that that the search operation in the southern Indian Ocean had concluded for the day.
“There were no sightings of significance,” a statement said.
“The search area experienced early sea fog particularly in the western areas, however conditions improved during the day.”
AMSA said the four military and four civilian aircraft involved in Sunday’s search effort had covered a total of 22, 780 sq miles south-west of Perth. Chinese military Ilyushin IL-76 aircraft and Japanese P-3C Orion aircraft would join the search on Monday, it added.
HMAS Success, an Australian navy supply ship, also took part in Sunday’s operation.
A key focus on Sunday was the sighting on Saturday of a wooden cargo pallet, along with belts or straps.
Mike Barton, operations co-ordinator at AMSA, said: “Part of the description was a wooden pallet and a number of other items which were nondescript around it and some belts of some different colours around it as well, strapping belts of different lengths.”
He added: “We tried to re-find that yesterday, one of the New Zealand aircraft, and unfortunately they didn’t find it. That’s the nature of it – you only have to be off by a few hundred metres in a fast-travelling aircraft.”
Pallets are used for shipping as well as plane cargo and Mike Barton urged caution, saying the sighting “could be anything”.
Earlier, Australian PM Tony Abbott said the sightings of objects were encouraging signs.
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