Later in the one-minute clip Mr Macron says: "You never listen to me" and the Crown Prince replies: "I will listen, of course".
Russia's state TV reported that Putin chose not to greet President Donald Trump, who was standing nearby.
But the warm reception Mr Putin gave Prince Salman is likely to inflame tensions rather than ease them.
The conversation between Macron and MBS took place in Buenos Aires as world leaders arrived in the Argentinian capital for the G20 summit.
Russian President Vladmir Putin and Saudi Crown Prince Mohammad bin Salman were very happy to see one another at the G20 summit in Buenos Aires on Friday. The Saudi royal followed up by patting the back of the Russian leader's hand.
Saudi-owned broadcaster Al Arabiya posted video on Twitter showing a cordial handshake between bin Salman and Chinese President Xi Jinping as the two held a bilateral meeting.
Trump, in an exclamation-heavy statement before the summit, said it did not matter whether Prince Mohammed knew about Khashoggi's death and that Saudi Arabia was important for business and for its hostility to Iran.
The killing has sparked widespread outrage but Western powers have pledged to maintain close relations with Saudi Arabia, a top oil producer and buyer of USA weapons.
Mr. Trump canceled his previously scheduled meeting with Putin on Thursday after he was briefed on the incident.
"They exchanged pleasantries at the leaders' session as he did with almost every leader in attendance", the White House official said on Friday.
With such a keen focus on the US President's trade policies, Mr Trump started the summit with what he certainly considers a win.
He also met with South Korean President Moon Jae-in, and Mexico's President Enrique Pena Nieto. The deal still needs to win congressional approval in Washington.