The French authorities allege that Noriega deposited profits from cocaine-trafficking, totalling about $3.15m, according to court papers, into French banks in the 1980s.
Noriega's lawyers had called for him to be sent to Panama instead, even though he has also been convicted there in absentia for crimes committed during his rule.
But another federal judge rejected that proposal last week.
Noriega's lawyers questioned why Panama, which has filed an extradition request, had not actively pursued it.
"Could it be that there are elements in the Panamanian government that do not want General Noriega's repatriation?" the defense team said in its petition.
The petition alleged there was "reason to believe that the French are seeking General Noriega's extradition as a quid pro quo for a $300m contract to sell high-speed trains to Panama".
The allegations were based on "statements by the French ambassador to Panama, Pierre Henry Guignard", the petition said.
Noriega, who ruled Panama from 1983 to 1989, was captured in the US 1989 invasion of Panama, ordered by president George Bush Snr, the father of the current US president.
The Panamanian leader had worked with the CIA for years, but eventually fell out of favour with Washington amid suspicions he was involved in drug-trafficking.
In 1992, Noriega was sentenced by a US judge to 40 years in prison for drug-trafficking, but the penalty was later reduced to 30 years and was shortened again for good behaviour.