"Our family calls on President Francois Hollande and the European Union to do everything possible to save Serge Atlaoui from the firing squad," his brother Andre told AFP, describing his "dismay" and "lack of understanding" at the court's decision.
Indonesia's Supreme Court on Tuesday rejected an appeal by Atlaoui on death row for drug offences, taking him and a group of other foreigners closer to execution by firing squad.
Serge Atlaoui, 51, was arrested near Jakarta in 2005 in a secret laboratory producing ecstasy and was sentenced to death two years later.
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.
He is one of several foreign drug convicts on death row in Indonesia who recently lost appeals for presidential clemency, typically a last chance to avoid the firing squad. They are expected to be executed once final legal appeals are resolved.
In a further bid to avoid execution, Atlaoui filed a request for a judicial review of his case at the Supreme Court.
However Suhadi, one of the judges assessing his case, said the court rejected his application on Tuesday.
"A panel of three judges has rejected (the request) for a judicial review from Frenchman Serge Atlaoui," said Suhadi, who goes by one name and is also the Supreme Court spokesman.
He said there was no new evidence presented — a requirement for a judicial review — and the reasons put forward were not sufficient.
Several other death row convicts also have legal bids outstanding, including two high-profile Australian drug traffickers who have lost several appeals but are now taking their case to the Constitutional Court, although authorities insist they have no more options.
A Ghanaian among the group is appealing to the Supreme Court.
The French ambassador to Indonesia warned last week that executing Atlaoui would have "consequences" for relations between Paris and Jakarta.
Australia has issued a similar warning.
"Neither France nor Australia can tolerate the death penalty being imposed on our citizens at home or abroad," Australian Foreign Minister Julie Bishop said in Paris after meeting her counterpart Laurent Fabius.
"We respectfully request that he (President Joko Widodo) show the same clemency towards the French and Australian citizens as Indonesia seeks other countries to show towards Indonesian citizens who are facing death row in other countries."
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.
However Indonesia has been actively trying to save its own citizens on death row abroad — Jakarta last week protested at the execution of two Indonesian women in Saudi Arabia.