He has been charged with laundering the equivalent of $2.8m from the Medellin drug cartel through French banks in the late 1980s.
Wrapping up the prosecution case on the final day of the trial, state prosecutor Michel Maes told the court: "We should retain the image of a perfectly structured organisation in the hands of one man, and in the interests of one man, Manuel Noriega.
"This system was conceived to launder drug money for Mr Noriega's profit."
Maes also demanded that all of Noriega's assets held in French accounts be seized.
Noriega's defence team argued that he should be acquitted, saying the allegations against him hinge on unreliable testimony from ex-drug traffickers paid and given protection by US authorities.
One of the lawyers, Yves Leberquier, urged the court to "go beyond the image that the United States present of Noriega" as a "dictator and cocaine-trafficker."
He said a 10-tear term would amount to a life sentence for Noriega, who suffers from partial paralysis and high blood pressure, meaning "the death in jail of an ill man of 76."
In 1999 a French court sentenced Noriega to 10 years in jail in his absence, but he was allowed to appeal that ruling in person after his extradition.
Noriega, who ruled Panama from 1983 to 1989, has already spent 20 years in a Miami prison for drug trafficking and money laundering and for years fought against being extradited to France.
A verdict is expected as early as next month.