France and the US have made efforts to end a row which started last week with the announcement of the Aukus defence pact between the US, UK and Australia.
The pact cost France a deal worth $37bn (£27bn) to build submarines for Australia.
Paris said it found out only hours before the public announcement.
The American and French presidents have now issued a joint statement saying the situation would have benefited from open consultations between allies.
Joe Biden and Emmanuel Macron spoke by phone for half an hour on Wednesday. They will also meet in Europe at the end of next month.
Announced last week, Aukus is widely seen as an effort to counter China’s influence in the contested South China Sea.
Analysts have described it as probably the most significant security arrangement between the three nations since World War Two.
But French anger over the pact had been palpable – the French foreign minister called it a “stab in the back”.
In a rare step among allies, Mr Macron had ordered the recall of the French ambassadors to Washington and Canberra.
However, the ambassador to Washington will now return to his post. There was no word on whether the ambassador to Canberra would do the same.
President Biden reaffirmed the importance of French and European engagement in the Asia-Pacific region.
And the statement underlined US recognition of the importance of stronger European defence to complement Nato – one of President Macron’s flagship projects.
US Secretary of State Anthony Blinken and the French Foreign Minister, Jean-Yves Le Drian, are expected to hold a bilateral meeting on Thursday on the sidelines of the UN General Assembly in New York, according to a US official.