The agreement, first reported by La Tribune, paves the way for political talks to resume among the project's three government backers, France, Germany and Spain, a source close to the matter told Reuters.
"The governments have received an offer from the companies to build the demonstrator for a new combat plane in the framework of FCAS," the French armed forces ministry said, adding that negotiations were continuing on the overall project.
The Future Combat Air System (FCAS) is designed to replace the German-Spanish Eurofighter and Dassault's Rafale with a combination of manned and unmanned aircraft from 2040.
First floated by German Chancellor Angela Merkel and French President Emmanuel Macron in 2017, the programme has been dogged by political differences as well as corporate disagreements.
It is also up against the rival BAE Systems-led Tempest fighter project involving Britain, Sweden and Italy.
A joint proposal from European defence group Airbus and Dassault still faces outstanding issues including intellectual property matters. Those must be addressed at the political level, Dassault boss Eric Trappier said last month.
Dassault accepts that Airbus will receive a larger overall FCAS workshare but remained ready to pursue a "Plan B" if the talks failed, the Dassault chief executive also said.
The industrial partners in the aircraft programme are Airbus on behalf of Germany, France's Dassault and Indra of Spain.
Separate negotiations have been taking place with engine suppliers Safran of France, MTU Aero in Germany and ITP, a Spanish subsidiary of Rolls Royce.
(Reporting by Tim Hepher, Tangi Salaun and Laurence Frost; Editing by Mark Heinrich and David Goodman)