The sum demanded equals the amount the French state has recovered from taxpayers who were UBS customers.
"Tax fraud is nothing other than robbery of the public community," prosecutor Eric Russo said at the end of a five-week trial which followed a six-year investigation into the Swiss banking giant and its French subsidiary
accused of abetting tax fraud and laundering proceeds between 2004 to 2012.
"Banks deserve to be put on trial and fined in line with the financial prejudice" they have caused, he told the court.
UBS has denied the charges.
France's national financial crimes unit estimates at least €9.76 billion ($11.2 billion) was not reported to the French tax authorities.
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 AG and its directors were perfectly aware they were breaching French law," Russo said.
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 AFP.
Not all these clients are suspected of tax fraud, the source said.
On Wednesday, Xavier Normand-Bodard, a lawyer acting on behalf of the state's civil interests, had called for UBS to be fined €1.6 billion.
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.
Normand-Bodard said that 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.