The preliminary probe was opened in March following an anonymous letter alleging that UBS had helped French clients evade taxes and move money overseas, according to the Charlie Hebdo weekly which first reported on the investigation.
The banking supervisor, which declined to comment on the report, has stepped up its monitoring of the bank, the weekly reported.
UBS rejected the allegations.
"The bank has neither initiated nor participated in any manner in any system to aid tax evasion," a UBS spokesman told AFP.
UBS paid a $708 million fine to the United States in 2009 to settle a tax fraud case which charged that which it helped US citizens open offshore accounts to avoid paying taxes while several thousand client names were handed over to end another US tax evasion probe.