The crown prince was filmed in an apparently tense conversation, telling the French president not to worry.
The Elysee said it was the first time that Macron and the crown prince, known as MbS, had spoken since Khashoggi's murder at the Saudi consulate in Istanbul on Oct 2.
Mr Trump later said there was "no discussion" but did not rule out holding longer talks with the crown prince during the two-day summit.
He might have been standing on the fringes of the traditional "family photo" at the Group of 20 summit in Argentina, but Saudi Crown Prince Mohammed bin Salman got lots of attention.
French President Emmanuel Macron told Saudi Crown Prince Mohammad bin Salman on Friday that Europe would insist on worldwide experts being part of the investigation into the murder of Saudi journalist Jamal Khashoggi.
The widely-shared video showed Salman replying: 'I will listen, of course.' It concluded with Macron saying: 'I am a man of my word'.
Mr Macron's office said the meeting with Mohammed bin Salman was justified because European nations wanted to send a united message about the need for probity in the investigation and were not going to sidestep an opportunity to reinforce that message during the G20.
Prince Mohammed also met Chinese president Xi Jinping on the summit sidelines, the Saudi Press Agency said on Twitter.
Mrs May is said to have told the Crown Prince to take action to prevent future incidents like the murder of Mr Khashoggi from happening.
There has been widespread condemnation and public outrage over attacks on sites such as school bus and hospitals, where Yemeni civilians, including children, have died.
After initially denying the murder, Saudi Arabia has acknowledged Khashoggi was killed inside the consulate but blamed his death on a "rogue" operation.
White House spokesperson Sarah Sanders insists the reason for the cancellation was the situation with Ukraine, but said the probe into possible collusion between the Trump presidential campaign and Russian Federation was damaging ties between the two countries.
The US president cancelled a formal sit-down with Mr Putin at the summit in Argentina over Moscow's seizure of Ukrainian vessels.
He is facing pressure from some leaders including the UK, France, Germany and Turkey's President Erdogan, who is also in attendance in Argentina, to admit exactly what happened.
U.S. President Donald Trump has made it clear that he doesn't want to jeopardize the longstanding relationship between Washington and Riyadh.