The prosecutor's office confirmed a report that first appeared in the French daily Liberation and said it was probing possible embezzlement and suspected "ill gotten gains".
The newspaper said Saleh's family had purchased apartments in high-rent districts of Paris near the Champs Elysees and Arc de Triomphe worth several million euros.
Ahmed Ali Abdullah Saleh, the late president's eldest son, was cited as being part of a property company created for the transactions.
Meanwhile, 30 million euros ($37 million) was transferred from Sanaa to a bank account opened by the son under another name in Paris, Liberation said.
The younger Saleh was head of Yemen's Republican Guard, an elite corps created by his father, and was also ambassador to the United Arab Emirates.
Assets of both father and son were frozen by the UN Security Council and the US Treasury Department in 2015.
French financial investigators were alerted by Swiss counterparts to suspicious financial transfers between Paris and Geneva, and launched a probe in 2019, the newspaper report said.
The prosecutor's office confirmed that the probe was still in progress.
The elder Saleh ruled Yemen for more than three decades before he was ousted in February 2012 following a popular uprising.
He was assassinated by Iranian-backed Houthi rebels in December 2017 at the age of 75.
