Google is one of several companies that have come under fire in Europe for paying extremely low taxes by shifting revenue across borders in an often complex web of financial arrangements.
"In regards to France, a €1.6 billion adjustment has been imposed on the company," the source told AFP, speaking as Google's CEO was in Paris.
Google declined to comment and the French finance ministry told AFP the amount the company would have to pay was subject to "fiscal confidentiality".
The figure emerged as Google CEO Sundar Pichai was in Paris, where he was set to meet Wednesday night with France's economy minister, Emmanuel Macron.
Speaking at the elite Sciences Po university in Paris before the tax demand hit the press, Pichai defended in general terms Google's tax practices.
"We're a global company. We have to abide by tax laws everywhere, we do abide by local tax laws in every single country," he said.
"We're advocating strongly for a simpler global tax system," he added.
France has previously refused to negotiate the amount of back taxes it would request.
However, a source inside France's tax authority said bargaining may still be possible.
"This does not mean that Google will ultimately pay 1.6 billion," the source told AFP.
"There will be appeals, and perhaps a negotiation in the end, in particular on penalties."
A deal last month between British tax authorities and Google was meanwhile criticised by a panel of British lawmakers who described the settlement reached as "disproportionately small" given Google's size and earnings.
Under the agreement, Google will pay £130 million ($185 million, €170 million) for a decade of Google business in Britain, where it makes 11 percent of its global sales.
Billions in fines
The company made profits of £106 million on revenues of £1.18 billion in Britain in the last 18 months alone and the Labour opposition party claimed the giant was paying only "three percent tax".
French Finance Minister Michel Sapin earlier this month said Google would not get a deal of that type on his side of the Channel.
"In France we would like to avoid an exceptional situation where there would be some type of flat-rate tax," he said.
Italy is also demanding Google pay over €200 million in back taxes following an inquiry by the financial police.
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The European Commission has cracked down hard on companies, including US icons such as Apple, Starbucks and Amazon, who have worked out arrangements with countries allowing them to slash their tax bills.
Swedish furniture giant Ikea has also been accused of underpaying taxes by one billion euros by using aggressive tax strategies in certain European countries.
Fights over tax bills are not the only trouble Google is contending with in Europe.
European competition officials have been investigating the US tech giant for years over alleged monopolistic practices involving its search engines, but any resolution has been elusive.
Three successive proposals by Google for an amicable settlement have been rejected.
If no agreement is reached and the group is found to have broken the EU's antitrust rules, it could face fines amounting to billions of dollars.