"If the Americans decide to go ahead and impose sanctions against the digital tax.in this case we would retaliate", Le Maire said, warning that - in some cases - the only alternatives to certain French goods are Chinese ones (paywall).
Seemingly trying to ease the tension, Mnuchin added that talks over the issue would be done in private, not on live television, and the key discussion is likely to be between U.S. President Donald Trump and British Prime Minister Boris Johnson.
At a meeting with Mnuchin on the sidelines of the World Economic Forum in Davos, Le Maire agreed to delay collecting a tax on multinational digital companies until the end of 2020.
However, he threatened tit-for-tat tariffs on the United Kingdom if it pressed ahead with plans for a tax on "Big Tech" companies.
"We now agree on a shared global framework", Le Maire told reporters at a briefing in Davos, Switzerland.
The US and European Union agreed to pursue a trade deal in July 2017 as a tentative truce after Trump had taken office and declared a war on America's yawning trade deficits with China and Europe. "This is good for us, and good for them".
After the meeting, Trump said the US would consider introducing tariffs on European auto imports if neither side could agree.
Huawei executive's extradition hearing to start in Vancouver
Soon after Meng's arrest, China detained two Canadians, former Canadian diplomat Michael Kovrig and businessman Michael Spavor. Meng was arrested at Vancouver International Airport in December, 2018, at the request of the Americans on fraud charges.
Mnuchin said at the World Economic Forum in Davos that he found the latest projections of the International Monetary Fund (IMF) - which trimmed its forecast for United States growth to 2.0 per cent this year and to 1.7 per cent in 2021 - to be overly pessimistic.
He argued a digital tax is "discriminatory in nature" and the U.S. is participating in the OECD process to find a solution.
The issue, which both sides indicated was resolved on Monday, has nonetheless been a lightning rod for a border transatlantic trade debate at the alpine conference this week.
The U.S. and China concluded a major trade deal this month after months of sometimes bitter negotiations, but Mnuchin said that the next round of talks could easily be broken into smaller parts, yielding several deals. "Digital companies will pay their fair tax in 2020", he said.
British Chancellor of the Exchequer Sajid Javid said in Davos on Wednesday that his government would focus on reaching a trade agreement with the European Union and an agreement with the United States, as it is in talks with Donald Trump's administration about the digital tax threat. Washington said Britain had insisted on implementing the measure in April.
The Organization for Economic Co-operation and Development, which advises the world's rich countries on policies, is trying to come up with an internationally agreed upon way to tax digital business. France pushed ahead with its tax when talks at the OECD level stalled a year ago.
The European Union talked up hopes for such an accord, while France signalled progress in a row over a new tax that seeks a fairer share of the titanic profits amassed by United States tech companies.