“We have responded positively to a request from the government of Malaysia,” deputy prime minister Xavier-Luc Duval said.
“Every effort will be undertaken to locate any debris.”
Coastguard ships were deployed Monday in the search, while appeals were made to private boats and fishermen to inform police if they sighted any possible wreckage, Mr Duval said.
In one of the most baffling mysteries in aviation history, MH370 inexplicably veered off course in March 2014 and disappeared from radars, sparking a colossal hunt that has until now proved fruitless.
In January, Malaysian authorities declared all 239 people on board presumed dead.
Last week a wing part washed up on the French Indian Ocean island of La Reunion, and has been taken to France to for physical and chemical analysis.
Already confirmed to be part of a Boeing 777, it is likely to have come from the doomed Malaysia Airlines flight, as no other such plane is known to have crashed in the area.
If the serial number on the flaperon confirms it is from flight MH370, the laboratory can then use sophisticated tools to try to glean more information about the causes of the crash, such as whether its shape corresponds more to a mid-air explosion or a crash into the ocean.
A fragment of luggage that was also found in the area is with the aircraft debris in France for specialist DNA testing.
