While a left-wing alliance won most seats, Macron appointed the conservative Barnier in a bid to reinstate stability.
But his government has been consistently undermined because it does not have a majority.
On Monday, Barnier opted to push through controversial reforms to social security by invoking presidential decree after failing to win enough support for the measures.
The budget bill sought to deliver €60bn (£49bn) in tax rises and spending cuts.
But Barnier was forced to cave in to changes demanded by critics due to his lack of a parliamentary majority.
He is now expected to become the shortest-lived prime minister in France’s Fifth Republic, with the left wing bloc in the National Assembly, as well as the far-right, predicted to back the motion against him.
If he does not survive the vote, he will remain in place as caretaker prime minister until Macron announces a new government.
While Macron – who is on a state visit to Saudi Arabia – has reportedly begun considering his pick for the next prime minister, the process could take weeks, as it did in summer.