The trial opened last autumn after seven years of investigations, launched when several former employees came forward with claims of unlawful conduct.
The move came as authorities across Europe cracked down on tax evasion and dubious banking practices in the wake of the global financial crisis which erupted in 2007.
The pressure eventually forced Switzerland to effectively end its tradition of ironclad bank secrecy, by joining more than 90 countries which agreed to automatically share more client account information among each other.
In the UBS case, French authorities determined that more than €10 billion had been kept from the eyes of tax officials between 2004 and 2012.
The National Financial Prosecutor's office urged a €3.7-billion ($4.2 billion) fine, the largest ever sought in France, saying the bank and its directors “were perfectly aware that they were breaking French law” by unlawfully soliciting clients and helping them evade French taxes.
They also sought a €15 million fine for UBS's French subsidiary, and fines of up to €500,000 for six top executives, including Raoul Weil, the former third-in-command at UBS, and Patrick de Fayet, formerly the second-ranking executive for its French operations.
In addition, lawyers for the French state, which is a plaintiff in the case, asked for €1.6 billion in damages.
UBS, which was ordered to post €1.1 billion in bail, has denied the charges and said its operations complied with Swiss law.
It also says that it was “unaware” that some French clients had failed to declare assets in Switzerland, and that prosecutors have not produced any proof, such as client names or account numbers, to back up their fraud claims.
The case is being closely watched by industry executives at a time when Paris and other European capitals are hoping to lure multinational banks from London as Brexit looms.
UBS is accused of organising or inviting prospective clients to prestigious outings such as the French Open or luxury hunting retreats, where UBS's Swiss bankers would meet their “prospects” — something they were not allowed to do under French law.
UBS France directors then used notes called “milk tickets” to keep track of how many “milk cans” – amounts of money – were transferred to Swiss accounts.
They say the system was merely a way to balance out bonuses due to French bankers who were effectively losing a client to their Swiss peers, and the notes were later destroyed.
But investigators claim the “milk tickets” were proof that UBS had a parallel accounting system for keeping the transfers off its official books.
Only one “milk ticket” was found during the inquiry, prompting defence lawyers to argue there was no proof to justify claims of a massive fraud.
Yet prosecutors pointed to the roughly 3,700 French UBS clients who later took advantage of an amnesty offer to regularise their tax declarations with the French authorities.
UBS has been embroiled in a series of similar cases, most notably in the United States, where the authorities said the bank used Switzerland's banking secrecy laws to help rich clients avoid taxes.
In 2009 it paid $780 million to settle charges it helped thousands of American citizens hide money from the Internal Revenue Service, and agreed to turn over information on hundreds of clients, severely denting Switzerland's long tradition of shielding banking clients and their operations from prying eyes.
That case was also prompted by a former American UBS employee turned whistleblower, Bradley Birkenfeld, whose book “Lucifer's Banker: The Untold Story of How I Destroyed Swiss Bank Secrecy” was published in 2016.
Last November UBS was again sued by US authorities, who accuse the bank of misleading investors over the sale of mortgage-backed securities in 2006 and 2007, just before the financial crisis struck.
UBS has denied the charges and said it will defend itself “vigorously”.