The summons came a day after Serge Atlaoui, 51, had an appeal rejected by Indonesia's Supreme Court, taking him closer to execution by firing squad for his role in a clandestine ecstasy lab near Jakarta.
Imprisoned in Indonesia for a decade, the father-of-four has always denied the charges, saying he was installing industrial machinery in what he thought was an acrylics factory.
His relatives have issued impassioned appeals in recent days, begging French President Francois Hollande and the European Union to save him.
Atlaoui is one of several foreign drug convicts on death row in Indonesia who recently lost appeals for presidential clemency.
They are expected to be executed once final legal appeals are resolved.
The French ambassador to Indonesia warned last week that executing Atlaoui would have "consequences" for relations between Paris and Jakarta.
Drug laws in Indonesia are among the world's toughest.
Widodo, who took office in October, has been a vocal supporter of putting drug traffickers to death, saying the country is facing a narcotics emergency.