Le Point wrote that the list of accounts has been handed over to the French tax investigators following searches at UBS.
The accounts were associated with French owners as the account number all ended in 111, a designation for France.
The 38,000 accounts contain various amounts ranging from 1,000 euros to more than one billion euros.
The names of people associated with the accounts are not yet known.
French tax investigators have been conducting a probe into alleged tax evasion since 2012 and UBS had to provide a security of 1,1 billion euros in 2013.
“There are no more secret accounts at UBS Switzerland since 2014, so the French authorities should already have the names of the owners,” the head of UBS France Jean-Frédéric de Leusse told Le Point.