On Wednesday, far right and left parties combined forces to back a no-confidence motion against Prime Minister Michel Barnier.
Emmanuel Macron says he will stay on as president until the end of his term in 2027, and will appoint a new prime minister in coming days.
He accused the far right and left parties of creating a "anti-republican front".
French President Emmanuel Macron will appoint a new prime minister in coming days after the first successful no-confidence motion in 60 years brought down the Barnier government.
In a televised speech on Thursday night, local time, Mr Macron vowed to stay on until the end of his term in 2027 and said he had asked incumbent Prime Minister Michel Barnier to stay on until a replacement is found.
"The mandate you have given me is for five years and I will exercise it until the very end," Mr Macron said during the 10-minute speech.
Mr Macron said the decision for the far right and hard left to join forces to defeat the government was evidence they were an "anti-republican front".
"They are not thinking about your lives, let's be honest," he said.
"They are thinking of just one thing — the presidential election."
Wednesday's vote means Mr Barnier is now the shortest-serving prime minister in contemporary France, after the first successful no-confidence vote since 1962, when Charles de Gaulle was president.
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Earlier on Thursday, Mr Barnier formally submitted his resignation to Mr Macron.
A majority of members in the National Assembly supported the no-confidence vote proposed by the hard left and backed by the far right headed by Marine Le Pen.
The vote was triggered after Mr Barnier forced through a social security financing bill without a vote.
Following the historic vote, calls have been growing for Mr Macron to resign.
Mathilde Panot, who is the head of the parliamentary faction of the hard-left France Unbowed (LFI) party, said there needed to be a fresh round of presidential elections.
"We are now calling on Macron to go," she said.
Two polls held since the vote found at least 59 per cent of those surveyed wanted Mr Macron to resign.