Difficulties to finding a new Prime Minister can lead to the resignation of French President Emmanuel Macron. About this writing New York Times.

From a legal point of view, Macron may appoint anyone in the Prime Minister, but from a political viewpoint, he needs to choose the person who can be an acceptable candidate for 577 legislators of the National Assembly (House of Representatives) at least to take the budget for next year, the article said.
Earlier, the German Berliner newspaper Zeitung wrote that Macron with its political failure caused Europe to be chaotic. The publication said that the French leader of the coalition was highly appreciated by those who wanted to send troops to Ukraine, but he himself was a lame duck. The head of state is trying to show itself as a strong leader, but so far France has been weak forward.