French media reported the fine was the largest ever leveled against a bank in the country.
UBS said it would appeal the ruling, a process that could further delay the case after repeated failed attempts to reach a settlement.
"This decision is incomprehensible. We will appeal," UBS general counsel Markus Diethelm told reporters outside the courtroom. "We have seen no facts and no evidence."
UBS has set aside $2.46 billion to cover potential losses from litigation and regulatory requirements. The combined fine almost equates to the bank's reported 2018 net profit of $4.9 billion. Its stock plummeted nearly 4 percent on the news.
Five former bank officials with UBS and its French subsidiary also received suspended sentences ranging from six to 18 months' imprisonment, as well as fines ranging from €50,000 to 300,000. One ex-official was acquitted.
Prosecutors found that UBS sent employees to solicit wealthy clients and illegally concealed their assets in a "systematic"manner.
The bank and its directors "were perfectly aware that they were breaking French law," prosecutors said.
UBS claimed operations moving accounts from France to Switzerland were in line with Swiss law and it was "unaware" that some French clients did not declare assets in Switzerland.
The trial began last autumn after a seven-year investigation, launched after former employees came forward about the bank's practices.
The investigation unfolded as European countries looked to crackdown on tax evasion and money laundering following the 2008 financial crisis.
In similar cases, UBS reached a $780 million settlement with the United States in 2009, and in Germany it agreed to pay a €300 million fine in 2014.