The contract was initially expected to be awarded this year and the delay had sparked Dassault and Airbus, the leading industrial partners in the project, to pressure France and Germany to make progress.
"There is no more issue right now between the French and German (governments) as far as the FCAS (Future Combat Air System) is concerned," Dassault CEO Eric Trappier told Reuters at the Dubai Airshow.
"There is an agreement at the top level and the next step should be the first contract for a demonstrator before the end of January 2020."
He also said talks between France's Safran and Germany's MTU Aero Engines, which are making the engines, were progressing and that he hoped an agreement would be reached this year.
The project to build a new generation of manned and unmanned warplanes was announced by the leaders of France and Germany two years ago and expanded earlier this year to include Spain.
Dassault and Airbus won a 65 million euro (£55.4 million) contract in January to develop the concept.
The first test fight of the demonstrator remains on track for 2026, Trappier said, having earlier warned that date could be at risk from delays to the programme.
The warplane system is expected to be operational from 2040, with a view to replacing Dassault’s Rafale and the four-nation Eurofighter, in which Airbus represents both Germany and Spain
"We are preparing not for the future of tomorrow but for the future of after tomorrow," Trappier said.
The European joint project faces competition from a British new generation fighter jet project dubbed "Tempest," which Italy joined last month.
Trappier said he did not mind that Britain was pursuing its own programme and that it could still join the Franco-German project, but only after the first demonstrator flight.
"What is sure is if nobody does anything, that is a problem. If there are two teams it's better than no team," he said.
Trappier also said he expected India to buy additional Rafale warplanes following its initial 36 jet purchase.
By Alexander Cornwell