"They want to make a deal and we'll see if we can make a deal. We're getting close," Trump told reporters at the G7 summit in Biarritz.
His comments come after he threatened to hit French wine with tariffs after Paris voted through the so-called Gafa digital tax, which he described as "very unfair".
The draft proposals are to be presented to the G7 heads of state later Monday.
The basic terms include a repayment by Paris of the difference between the French tax and a new system to be put in place by the Organisation for Economic Cooperation and Development.
American trade representatives and others close to the Trump camp at the Biarritz summit are said to have accepted the new terms.
When the tax on the local profits made by US-based internet companies was first proposed by Emmanuel Macron, US leader Donald Trump reacted by threatening a huge increase in import taxes on French wines entering the United States.
More details on this story as they become available.