For the prince, it's about the killing of a dissident Saudi journalist in the country's Istanbul consulate.
It's possible to make out Prince Mohammed saying "Don't worry", to which the French President responds "I am worried".
The Elysee official said it was the first time Mr Macron and the Crown Prince, known as MbS, had spoken since Khashoggi's murder at the Saudi consulate in Istanbul on October 2.
Mr. Trump for his part has so far kept his distance from both Putin and the crown prince at the G-20.
The content of the gruesome tape - a key piece of evidence in the murder allegedly ordered by United States ally Saudi Crown Prince Mohammed bin Salman - was distributed by Turkey after Khashoggi was killed inside the Saudi consulate in Istanbul on 2 October.
As world leaders get down to business at the G20 in Buenos Aires, tensions over trade, security and climate change already threaten to leave it the third such multilateral meeting this year to fail to agree a joint communiqué, following in the footsteps of the G7 and APEC summits.
The Crown Prince also discussed with Modi Saudi oil giant Aramco's investment in refineries in India, including the company's project to build a large refinery on the western coast of India, SPA said.
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Later in the one-minute clip posted on Twitter, Macron is heard saying, "You never listen to me", to which bin Salman replies, "I will listen, of course", as they were standing close together and apparently unaware their conversation was being recorded.
Macron told Prince Mohammed that Europeans wanted global investigators to take part in the probe on Khashoggi's death and stressed "the necessity of a political solution in Yemen", the Elysee Palace said.
Furthermore, the English-language Saudi Gazette shared a video of the meeting reportedly showing a cryptic exchange between the pair on the killing of Khashoggi.
The US Senate nonetheless moved this week to end support for the Saudi-led war against rebels in Yemen amid outrage over attacks on civilian sites including a school bus and hospitals. Saudi Arabia claims that the prince had no prior knowledge of the murder.
The US president cancelled a formal sit-down with Mr Putin at the summit in Argentina over Moscow's seizure of Ukrainian vessels.
"They exchanged pleasantries at the leaders' session as he did with almost every leader in attendance", the White House official said on Friday.
Instead the US president appeared to barely acknowledge MBS, as he's known, before taking his place for the photo between French President Emmanuel Macron and Japanese Prime Minister Shinzo Abe.