Frederic Chatillon, whose company Riwal ran communications for the far right Front National (FN) party's election campaigns in 2012, said all his transactions were legitimate.
About â‚¬316,000 ($360,000; Â£250,000) was moved from Riwal in 2012 through Hong Kong, Singapore, the British Virgin Islands and Panama, Le Monde reported.
The FN says it was not involved.
The party "will not tolerate outrageous associations that are made", it said.
Panama Papers reaction - latest
Q&A on Panama Papers
The BBC and French newspaper Le Monde are among more than 100 media partners chosen to analyse parts of 11m files from the secretive Panamanian law firm Mossack Fonseca that were leaked and released on Monday.
Le Monde said the aim of transferring the money from Riwal was to "get money out of France, through shell companies and false invoices".
A former FN official was also named in the leaked files in connection with the transfer from Riwal, Le Monde reported.
Mr Chatillon told French media (in French) that he and his shareholders had decided to invest in Hong Kong "because Asia offered the most attractive profitability prospect".
But Mr Chatillon said any subsequent decision to send money on to shell accounts in Panama managed by Mossack Fonseca was made without his knowledge.
"Clearly, this private matter has nothing to do with the Front National," he added.
Mossack Fonseca says it has operated beyond reproach for 40 years and has never been charged with criminal wrong-doing.
In other global reaction:
Eleven million documents held by the Panama-based law firm Mossack Fonseca have been passed to German newspaper Sueddeutsche Zeitung, which then shared them with the International Consortium of Investigative Journalists. BBC Panorama and UK newspaper The Guardian are among 107 media organisations in 76 countries which have been analysing the documents. The BBC does not know the identity of the source.
A French businessman named in leaked files from a Panama law firm has denied deliberately funnelling money offshore.