The Paris prosecutor’s office is acting after far-right candidate Marine Le Pen suggested front runner Emmanuel Macron had an offshore account in the Bahamas.
Mr Macron has filed a complaint following the accusation during a TV debate on Wednesday night.
On Thursday Mr Macron accused Ms Le Pen of spreading “fake news” and said he never held a bank account “in any tax haven whatsoever”.
A member of Mr Macron’s camp has since claimed he has been the victim of a “cyber misinformation campaign”.
Ms Le Pen appeared to backtrack when asked on French TV whether she was formally accusing Mr Macron of having a secret offshore account. She replied: “Not at all.
“If I wanted to do so I would have done it yesterday. I’ve just asked him the question. If I had proof, I would have claimed it yesterday.”
The latest opinion polls show the pro-EU Macron holding a strong lead over Ms Le Pen ahead of Sunday’s run-off vote.
The independent centrist received the endorsement of former US president Barack Obama on Thursday.
In a message posted on Mr Macron’s Twitter account, Mr Obama said: “I’m not planning to get involved in many elections now that I don’t have to run for office again, but the French election is very important to the future of France and the values that we care so much about.”
The two candidates sparred during a live standoff watched by up to 20 million people in France.
Their sharpest exchange was over national security – a sensitive subject in a country that has suffered a string of terrorist attacks in recent years.
Ms Le Pen accused Mr Macron of having no plan on security and of being soft on Islamic extremism.
He told her that radicals would love her to become president because she would stoke conflict.
Mr Macron accused Ms Le Pen of being capable of starting a civil war.
Ms Le Pen also played up Mr Macron’s background as a former banker and economy minister in the outgoing Socialist government.
She said he was the “candidate of globalisation gone wild”; he called her a parasite a “parasite” and a liar.