Macron had suggested a “new method” to put together an executive, Greens chief Marine Tondelier said after meeting him at his Elysee Palace office.
After July’s snap elections produced no clear majority, Macron took almost two months to name conservative Barnier as premier.
He was then toppled last week in a no-confidence vote over a cost-cutting draft budget for 2025 meant to tackle France’s yawning deficit.
New polls are ruled out until the summer, leaving Macron this time around to call for a “meeting of different political forces to discuss a platform” that could unite them in government, Tondelier said.
Until now, Macron had only been meeting party leaders individually.
Macron was “very clear about the fact that as far as he is concerned, the RN is not within the circle of parties willing to talk”, Tondelier said on Monday.
The RN had initially helped prop up Barnier’s minority government before supporting his downfall.
It leaves the left, centre and centre-right to try and find common ground after clashing fiercely ever since Macron’s first presidential win in 2017.