The Swiss banking giant has been on trial in Paris since early October following a six-year investigation which alleged that UBS and its French subsidiary laundered proceeds from tax fraud carried out from 2004 to 2012.
UBS has denied the charges.
Xavier Normand-Bodard, a lawyer acting on behalf of the French state, on Wednesday asked the court to punish the bank for pretending not to know its French clients hid assets in Switzerland to defraud French tax authorities.
Six bank managers and former managers are also on trial, including Raoul Weil, the former third-in-command at UBS, and Patrick de Fayet, formerly the second-ranking executive for its French operations.
France's national financial crimes unit estimates at least €9.76 billion ($11.2 billion) was not reported to the French tax authorities.
Normand-Bodard said as of September 30, 2015, a total of 3,983 French taxpayers who had held accounts at UBS had filed amended tax returns, turning over an extra €3.7 billion in taxes.
"This laundering system has been operating for years," the lawyer said, adding that while international agreements now require banks hand over data this did not mean previous actions should be amnestied.
"They have to be made accountable," he said.
The inquiry was opened after a former employee alerted authorities over the bank's alleged system of setting up dual bookkeeping to hide the movement of capital into Switzerland.
The bank's staff allegedly approached French clients, from wealthy businessmen to sports stars, at receptions, golf and tennis tournaments or concerts to convince them to hide their money in Switzerland.
The Swiss bank says it was "unaware" that some French clients had failed to declare assets in Switzerland. It said the law did not require them to check on clients' tax position in their home countries.
UBS has already been found guilty of conspiring to help some 20,000 clients hide billions of dollars from US authorities from 2002 and 2007. The bank paid $780 million to settle to the case.
According to documents provided by German authorities to French investigators, deposits from some 38,000 French clients with UBS amounted to a total of around 13 billion Swiss francs (€11 billion, $13 billion), a source close to the case told the AFP news agency.
Not all these clients are suspected of tax fraud, the source said.