France and the US have made efforts to end a row which started last week with the announcement of a defence pact between the US, UK and Australia.
The Aukus pact cost France a submarine contract worth billions of dollars.
In a 30-minute phone call on Wednesday, the French and US presidents agreed to try to find a way forward.
The US acknowledged that the situation would have benefited from "open consultations", and France agreed to send its ambassador back to Washington.
In a carefully worded joint statement, the two governments said US President Joe Biden and French President Emmanuel Macron would "open a process of in-depth consultations, aimed at creating the conditions for ensuring confidence".
The two leaders are set to meet in Europe at the end of next month.