Prosecutors in France are investigating the role that one of the country’s largest banks played in the transfer of $2 million that they believe was a bribe to ensure Rio de Janeiro won the rights to host the 2016 Summer Olympics, according to documents seen and verified by The New York Times.

The documents, which outline the case sent by a French investigator to prosecutors in Brazil, suggest that the bank, Société Générale, might have breached money-laundering regulations.

Société Générale said in a statement that it complies with industry standards pertaining to money laundering regulations and so-called know-your-customer rules, which all major banks are expected to follow.

“The Group considers the fight against corruption and money laundering as a top priority,” the statement said, adding that the bank does not comment on individual cases.

Payments from a deep-pocketed Brazilian businessman to the son of an influential former International Olympic Committee member days before Rio in October 2009 was surprisingly picked to host the Games were routed to Société Générale accounts, according to the documents. The accounts were linked to Papa Massata Diack of Senegal, whose father, Lamine Diack, led track and field’s governing body for 16 years through 2015.

The Diacks and the businessman, Arthur Cesar de Menezes Soares Filho, whose holding company made the payments, have been accused of corrupting the voting process that took the Olympics to South America for the first time. Investigators want to know whether Société Générale acted lawfully when Soares attempted to transfer funds to the younger Diack.

Soares could not be reached for comment. His whereabouts is unknown.

The sprawling, French-led investigation into the attribution of major sporting events, including the 2020 Summer Olympics in Tokyo and several track and field championships, has not formally implicated any banks or bankers. The allegations have similarities with the decades-long global soccer corruption schemes unmasked by United States authorities in May 2015, which led to the arrests of several senior officials for trading their influence for millions of dollars in bribes and kickbacks.

In the soccer corruption case, American authorities have scrutinized numerous banks through which bribe payments traveled, but none of those financial institutions have been publicly charged. One Swiss banker, however, has been convicted of money laundering conspiracy for having facilitated the transfer of tens of millions of dollars in bribes and kickbacks to soccer officials.

Nine days before I.O.C. members gathered in Copenhagen, Denmark, to declare Rio the winner in a competition that also included Chicago, Madrid and Tokyo, Soares’s company, called Matlock, attempted to transfer $2 million from an account it held in the British Virgin Islands to a Société Générale account in France controlled by Papa Massata Diack, according to the documents. Five days later, on Sept. 28, the money was sent back by the bank. Under French law, the bank should have reported the transaction with Tracfin, a national watchdog for suspicious transactions.

On Sept. 29, Soares used a Matlock bank account in Miami to make two separate payments totaling $2 million to accounts held by Papa Massata Diack directly or by his company Pamodzi Consulting. Those accounts were in Société Générale-affiliated banks in Russia and Senegal, where Diack is currently living.

“Analysis of these flows suggests that the first transfer, due to its amount and its geographical origin, could be blocked in France in application of anti-money laundering rules,” according to the documents.

“This would explain why it was immediately followed by split transfers on behalf of the same company based in Miami, from another bank account, to two subsidiaries of the Société Générale based in countries that were more complacent in the matter of anti-money laundering.”

In their communication with their Brazilian counterparts, the French prosecutors said they had yet to determine “the level of involvement of the bank.”

It is unclear what level of cooperation the bank has provided. Since July, the investigation has been transferred from the Parquet National Financier, France’s financial crimes investigator, to magistrate Renaud van Ruymbeke, a specialist in financial corruption.

Van Ruymbeke traveled to Rio last month and was present when the authorities there raided the home of Carlos Arthur Nuzman, the longtime head of Brazil’s Olympic Committee, and a crucial architect of the 2016 bid. Authorities accused Nuzman of being the central pillar of a scheme — along with the former Rio governor Sergio Cabral and Soares — to buy votes from African members of the I.O.C.

The African votes would have represented about 10 percent of the total cast for Rio in 2009. The city’s bid had the lowest technical score from the I.O.C. of the four final bidders in Copenhagen. It beat out Madrid by 66-32 in a final round of voting after Chicago and Tokyo had been eliminated.

“Nuzman was the agent responsible for bringing together interested parties, making contacts and oiling relationships to organize the mechanisms for transferring Cabral’s bribes directly to African members of the International Olympic Committee, which was effectively done by way of Arthur Soares,” Rio prosecutors said in a statement at the time. Nuzman has emphatically denied any involvement. He has not been arrested.

Soares is the subject of an international arrest warrant; Cabral is serving 45 years in prison for a string of corruption-related crimes, including some tied to projects linked to the Olympics and soccer’s World Cup, held in Brazil in 2014.

Winning the Olympics was hailed by Rio’s bid leaders as an unparalleled opportunity to transform the city on a scale not seen in decades, and to improve the lives of millions of the coastal metropolis’s poorest citizens. Instead it turned into “an enormous trampoline for corruption,” the Brazilian prosecutor Fabiana Schneider said last month. Going into the final vote for selection, Rio was not considered the favorite but won, according to Schneider, despite being “the worst candidate.”

Investigators have tracked several transactions made from the Société Générale-affiliated accounts linked to Papa Massata Diack, including on the day Rio was picked to host the Olympics. They include more than $250,000 to jewelry businesses in Paris and Qatar. Diack has strongly denied the accusations against him, calling them “the biggest lie in the history of world sport.” His father, now 84, has been held under arrest in France since 2015.

Failing to alert authorities to suspicious transactions can result in financial penalties for banks. In July, in a separate case, French banking regulators fined Société Générale nearly $6 million for inadequate anti-money laundering controls.