Bruno Le Maire told journalists that a meeting in Berlin Friday with his German counterpart Olaf Scholz had been useful.
“I think a compromise in the coming weeks is possible and we will be able to send the clear message that we agree on a fair taxation of the internet giants,” he added.
“We made real progress today. I remain confident that we can deliver by the end of the year.”
The two ministers met for four hours to discuss a controversial EU proposal to slap a European tax on US tech giants.
The EU proposal is for a rapid three-percent tax on revenue generated by certain kinds of activities, such as online advertising or the selling of personal data.
France has been pressing its EU partners to sign up to such an initiative, but Germany has until now been among the sceptics.
Scholz has come out in favour of a global minimum fiscal regime for multinationals, but media reports suggest he is not yet convinced by the digital tax proposal from the EU.
Germany's concern is that such a measure, which would target companies such as Google, Amazon, Facebook and Amazon, would provoke retaliatory measures from the United States. Berlin would rather see an agreement in the framework of an international organisation such as the OECD.
According to one source close to Friday's ministerial talks, a compromise under discussion is for the tax to be agreed in principle by the end of the year, but not implemented for 12 to 24 months.
Approached by AFP, Germany's finance ministry has not so far commented on the talks.
Ireland and several northern European countries who are hosting the European bases of the tech companies targetted, are not happy about the proposals.