France's Finance Minister Bruno Le Maire told France 2 television on Thursday that he would give himself "until March" to reach a deal with other EU members on a digital tax.
France had been hoping to reach an agreement on the issue by 31 December.
"I'm not letting anyone get away", said Le Maire.
"The money is with the internet giants who make considerable profits thanks to French consumers. They [the companies] pay 14 points less on the income tax scale than other small and medium companies."
On Tuesday, at an EU finance ministers meeting in Brussels, France and Germany agreed on a scaled-back version of the tax in a bid to overcome significant opposition to the plan among some of their EU neighbours.
European tax rules require unanimous backing by all EU members.
Under the new plan, presented as an interim solution while waiting for a global deal brokered by the OECD, digital giants would pay a three-percent levy on online advertising sales.
Resistance from Ireland, Nordic countries
If the plan comes into force, at a European level, the tax could bring in 1.3 billion euros per year, according to the French finance ministry, compared to the four or five billion euros initially expected by the government.
The measure, set to come into force in 2021 if a global plan has not been agreed by then, would chiefly target Google and Facebook, which dominate the online advertising market in Europe.
However, Ireland, which hosts the European headquarters of several US tech giants, and leads a small group of otherwise mostly Nordic countries, says the tax will punish European companies and stoke Washington's anger.
Germany, which firmly backed the plan at first, also expressed reticence after auto giants expressed concern it could damage their digital business models.
Some measures to tax Gafa and other digital heavyweights have already been taken at a national level in several countries including the UK and Singapore.