"I call on you to undertake a long battle."
The organisers said about 300,000 people demonstrated peacefully across France, including 160,000 in Paris, although police in the capital said 26,000 people had protested in the city.
The Interior Ministry did not immediately give a figure for the entire country, but its numbers are usually much lower than those given by organisers.
Barnier meanwhile made his first official visit, meeting staff at a Paris hospital. The worsening condition of the public health sector has been one of the areas that people have demanded action after months of procrastination.
"Without carrying out miracles, we can make improvements," Barnier, who lacks a clear majority, told reporters.
He said on Friday he wants to include conservatives, members of Macron's camp, and some from the left in his future government.
But he faces the daunting task of trying to drive reforms and pass the 2025 budget with the threat of a no-confidence vote hanging over him at the start of October, when he is due to outline his policy objectives to parliament.
DENIAL OF DEMOCRACY
France is under pressure from the European Commission, the European Union's executive body, and from bond markets to reduce its deficit.
The left, led by LFI, has accused Macron of a denial of democracy and stealing the election, after Macron refused to pick the candidate of the New Popular Front (NFP) alliance that came top in the July vote.
Barnier's centre-right Les Republicains party is only the fifth bloc in parliament with less than 50 lawmakers, and the left believes he will push wholesale spending cuts and a tougher stance on immigration.
Across 130 locations in France, people carried banners attacking Macron for betraying them and called on him to be impeached.
"He (Barnier) has no social conscience and will constitute a government which will be in the same line as the previous ones. So that is enough now," civil servant Jeanne Schmitt, 45, told Reuters on the sidelines of the Paris march.
Pollster Elabe published a survey on Friday showing that 74% of French people considered Macron had disregarded the results of the elections, with 55% believing he had "stolen" them.
Barnier continued consultations on Saturday as he looks to form a government, a tricky job given he faces a potential no-confidence vote.
NFP and the far-right National Rally (RN) together have a majority and could oust the prime minister through a no-confidence vote should they decide to collaborate.
The RN gave its tacit approval for Barnier, citing a number of conditions for it to not back a no-confidence vote, making it the de facto kingmaker for the new government.
"He is a prime minister under surveillance," RN party leader Jordan Bardella told BFM TV on Saturday. "Nothing can be done without us."