The cabinet was appointed at the weekend after President Emmanuel Macron and Barnier struggled to put together a team following a snap election in early July that delivered a hung parliament.
"Focus on action rather than talk," his office quoted Barnier as telling the ministers ahead of a cabinet meeting in the afternoon. "No theatrics."
Barnier said they must show respect for all their compatriots and political parties, listen to everyone and be humble.
Opinion polls and elections have for years shown that voters are unhappy with Macron's top-down style of power.
While an alliance of left-wing parties topped the July election and the far-right National Rally (RN) was the single party with the most votes, Macron's centrists eventually struck a deal with the center right and conservatives to form a government.
The ministers in Barnier's new cabinet, including the finance and budget ministers, are mostly little known to the French public and many have little political clout.
One exception is new Interior Minister Bruno Retailleau, 63, a veteran from The Republicans (LR) conservative party, and a driving force behind the party's rightward shift.
"The French people want more order - order in the streets, order at the borders," Retailleau said as he took office.
He said he would be hard on those who attack or disrespect politicians, and would also take a tough stance on antisemitism.
KINGMAKERS
How stable the new government will be, and whether it will manage to get reforms adopted by parliament, remains to be seen.
The RN is in a kingmaker position after it gave tacit support to Barnier's premiership but reserved the right to back out if its concerns over immigration, security and other issues were not met.
Retailleau has long called for much stricter policies on immigration but on Monday he did not spell out what his policies on that front would be.
"We will be the ones deciding whether this government has a future or not," RN lawmaker Jean-Philippe Tanguy told France Inter radio, adding that they would wait to see what Barnier will announce in his speech scheduled for Oct.1.
Barnier on Sunday opened the door to raising taxes on France's wealthiest individuals and some big corporations to help close a gaping hole in the public finances, but said he would protect the lower and middle classes.
Despite the entry of 10 politicians from the Republicans in cabinet, Macron kept a number of outgoing ministers in key posts. Only one left-wing politician joined the cabinet, Didier Migaud as justice minister.
