The law will cover companies that have global revenue of more than €750 million and French revenue of more than €25 million.
It will be applied from the beginning of this year and is expected to raise about €400 million.
France made its intentions clear last year, with Finance Minister Bruno Le Maire telling the media in December that €500 million (US$570 million) would be raised through this measure in 2019.
Reacting to Lighthizer's comments, Le Maire said France was "sovereign and decided its own tax rules".
"I want to tell our American friends that this should be an incentive for them to accelerate even more our work to find an agreement on the international taxation of digital services," he said.
Other countries have taken similar steps with the UK having put in place a digital services tax which will take effect from April 2020.
The French law, which targets companies that use the data of consumers to sell online advertising, is expected to hit Airbnb and Uber as well as companies from China and other parts of Europe.