French news weekly L'Express is reporting that Apple has paid nearly 500 million euros to resolve the case in a confidential settlement reached in December.
Apple declined to disclose the amount paid but said in a statement that the French
tax administration had recently concluded a multi-year audit and that "an adjustment" would be published in its public accounts.
The company added that it recognised the important role taxes play in society.
French authorities declined to comment further, citing the confidentiality of tax matters.
Apple is one of several US technology giants targeted in Europe over their tax strategies, which see them route their income through low-tax nations such as Ireland or Luxembourg.
In 2016, Apple was ordered by the European Commission to pay 13 billion euros in back taxes to Ireland.
The new deal in France comes as the government prepares to push ahead with its own unilateral "GAFA tax" (named after Google, Apple, Facebook and Amazon) faced with the failure of EU members to agree on the subject.
The tax, to be put to the French parliament in a bill later this month, would affect companies with global sales of more than 750 million euros and 25 million euros in France.
It would be retroactive to January 1 and is expected to raise 500 million euros this year.
Apple is the second major technology company to reach a tax deal with French authorities within the past year, reflecting the growing pressure from voters on governments to bring foreign companies to book.
French Economy Minister Bruno Le Maire has called the question of how and where global companies pay their taxes "a major issue in the 21st century".
According to L'Express, the deal between France and Apple was clinched after several months of talks, and concerned the small amount of revenue the firm booked in France while the sales it reported in Europe ballooned.