"France believes that the efforts of the International Criminal Court are capable of establishing the facts that have led to this crisis and thus contribute to finding a solution," a statement by President Emmanuel Macron's office said on Saturday evening.
Paris is "deeply worried" by the situation there and called on President Nicolas Maduro's government to open dialogue with the opposition, it went on.
The foreign ministers of Canada, Argentina, Chile, Colombia, Paraguay and Peru on Wednesday announced that they had written to the court calling for an investigation into "crimes against humanity".
Argentina's Jorge Faure claimed there was evidence of "arbitrary detention, extra-judicial executions, torture, sexual assault, rapes" and other "flagrant rights abuses".
Venezuela is increasingly isolated in Latin America, as economic and political crisis deepens there and thousands flee to neighbouring countries to escape hyperinflation and shortages.
During this week's UN General Assembly meeting, US President Donald Trump declared that "all options are on the table" and raised the possibility of a military coup against Maduro.