Jean-Luc Mélenchon, a senior agitator for the radical French Submission party, called for “the strongest possible mobilization” in a national demonstration.
About 130 protests are taking place, with the largest starting Saturday afternoon in central Paris.
Mr. Mélenchon took part in the Paris protests, giving a speech from atop a float with the slogan “Stop Macron's coup for democracy.”
Protesters are also using slogans such as “Democracy rejected” and “Stolen elections”.
Left parties are furious that their pick for prime minister, Lucy Castes, has been rejected by President Macron, who has said she has no chance of surviving a vote of confidence in parliament.
Mr Barnier looks set to survive the vote of confidence, as the far right, which also holds a large number of seats, has said it will not automatically vote against him.
This has led to criticism that his government will become more reliant on the far right.
“We have a prime minister who is completely dependent on the National Rally,” Ms. Castes said.
Mr Barnier visited a children's hospital in Paris on Saturday afternoon and stressed the importance of public services, but told health workers the government “will not perform miracles”, local broadcaster BFMTV reported.
