Chinese officials have so far made no public comments on the issue.
Mr Meng is a senior Communist Party official in China.
What is the French investigation looking at?
It was opened after Mr Meng's wife went to police to report her husband missing.
She said she has not heard from him since his departure on 29 September.
Police sources said their investigation was into what is termed in France a "worrying disappearance", Reuters reports.
Has Meng Hongwei angered China?
Analysis by BBC Asia Editor Celia Hatton
Meng Hongwei's disappearance seems to fit in with a now familiar pattern among China's senior Communist Party officials. The official in question suddenly drops out of the public eye and an alarm is raised that the person is "missing", usually by members of the public.
Eventually, the party issues a terse statement that the official is "under investigation", the official is then booted from the party for "disciplinary infractions" and - eventually - a prison sentence is announced. Since Xi Jinping came to power in 2012, well over a million party officials have been disciplined in some way.
Mr Hongwei's case is notable for a few reasons. First, his wife notified the French authorities after he had only been missing for a few days. Family members of missing party officials rarely, if ever, reach out to foreign authorities, in fear their relatives will face ever greater punishment.
Did the wife do this because she felt there was no other option? Also, at one time, China prized Mr Meng's lofty position at Interpol.
If he has really gone missing within the Chinese state apparatus, who did he anger, or what could he have done for Beijing to willingly, and publicly, forfeit the top job at Interpol?
How has Interpol reacted?
In a statement, the organisation said it was aware of reports of the "alleged disappearance" of Mr Meng.
"This is a matter for the relevant authorities in both France and China," it said.
Interpol added that the secretary general - not the president - was in charge of the day-to-day running of the 192-member organisation
As president, Mr Meng leads the Executive Committee, which provides the overall guidance and direction to Interpol. Mr Meng's term is scheduled to run until 2020.
Before taking over at Interpol, Meng Hongwei was deputy minister in charge of public security in China.
After his election human rights groups expressed concern that the move could help China pursue political dissidents who have fled the country.
Elected as Interpol's president in November 2016
Scheduled to serve until 2020
Is a senior Communist Party official in China and has served as Chinese vice-minister of public security
Has 40 years of experience in criminal justice and policingBut Mr Meng said at the time that he was ready to do "everything he could towards the cause of policing in the world".
Mr Meng has 40 years of experience in criminal justice and policing in China, notably in the fields of drugs, counter-terrorism and border control, according to Interpol.
Interpol can issue a red notice - an international alert - for a wanted person.
But it does not have the power to send officers into countries to arrest individuals, nor issue arrest warrants.