Amazon is in a dispute with the French authorities over the amounts involved and is ready to take legal action if necessary, the company says in a document filed to the Securities and Exchange Commission (SEC).
The document has been posted on the US stock market regulator's website.
The back taxes, penalties and interest that the French are seeking from Amazon relate to earnings in France for the years 2006-10 and "the allocation of income between foreign jurisdictions."
Amazon reduces its exposure to corporation tax in France and most of the rest of Europe by reporting European sales through a Luxembourg-based holding company, taking advantage of the tiny Duchy's relatively generous taxation of non-domestic earnings.
This arrangement allowed Amazon to pay a tax rate of 11 percent on foreign profits last year - roughly half the corporation tax it would pay, on average, in neighbouring countries. France typically taxes the net profits of companies at 33 percent.
Television station BFM Business reported that Amazon had paid 3.3 million euros ($4.2 million) in taxes in France for 2011, based on reported sales of 110 million euros which were less than a tenth of actual sales estimated at 1.3 billion euros.
Amazon executives rarely make public comment on the arrangement but the company has insisted in the past that it is completely legal under European Union's single market rules.
In its statement to the SEC, the company said: "We disagree with the proposed (French) assessment and intend to vigorously contest it.
"We plan to pursue all available administrative remedies ... and if we are not able to resolve this matter with the (French), we plan to pursue judicial remedies."
The emergence of a dispute between the US multinational and the French authorities emerged a day after Amazon's public policy chief in Europe, Andrew Cecil, was grilled by British MPs who believe the company should be paying much more tax there.
Cecil angered the lawmakers by failing to answer straightforward questions about the company and its earnings amid reports that Amazon's UK unit paid less than $2 million in taxes last year on sales estimated to be close to $10 billion.
Cecil was unable to explain the corporate structure of the group and admitted not knowing who owned the Luxembourg holding company.
The parliamentary committee, which is also examining the tax affairs of Google and Starbucks, slammed his evasive responses as unacceptable and said it would be summoning a more senior Amazon executive to answer their questions.
It is not just in Europe that Amazon has run into problems with the tax authorities.
In its statement to the SEC, it revealed that US and Japanese tax authorities had reached an agreement on the allocation of the company's earnings between those two countries for 2006-12. The cost to Amazon of this settlement was "not significant", it said.
The company however also revealed that it remains under investigation by the US Internal Revenue Service over its tax returns for 2005 and 2006.
It also admitted that there was a chance of the company being hit by demands for taxes dating back to 2003 in "various states and other foreign jurisdictions" including China, Germany, Luxembourg, and Britain.