Last year France approved a levy on the firms such as Google, Apple, Facebook, Amazon and Netflix as international efforts failed to find a new approach to taxing money coming from online sales and advertising.
In December, US President Donald Trump threatened to punish Paris with duties on more than 2 billion euros worth of French wines, cosmetics and leather handbags if it pursued its plan.
Le Maire said he had urged calm during a long telephone call with Mnuchin over the spat.
"We have given ourselves exactly 15 days to solve the issue at the Organisation for Economic Cooperation and Development," Le Maire said.
- France cautions US against punitive tax tariffs for its new digital tax
- Amazon to pass cost of France's new digital tax onto French customers
Urging Washington not to impose sanctions during the talks, Le Maire told France Inter radio: "This trade war is in no one's interest and I call on our American friends to display wisdom, to return to their senses."
The proposed tax will lead to the tech companies forking out up to three percent of their revenues earned in France.
Washington says US companies have been singled out by the French tax.
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