Barnier, 73, led the EU's talks with Britain over its exit from the bloc from 2016 to 2021.Â
Before that, the conservative politician held roles in various French governments and was also EU Commissioner.
Macron had considered a string of potential prime ministers in recent weeks, none of which mustered enough support to guarantee a stable government, and there is no guarantee Barnier's government will manage to get reforms adopted by a hung parliament.
But at least the far-right National Rally (RN), whose party is one of the biggest in parliament after the early July election, signalled earlier on Thursday it would not immediately reject Barnier if he met certain conditions.
Barnier is a staunch pro-European and a moderate career politician, but he toughened his discourse considerably during his failed 2021 bid to get his conservative party's ticket for the presidential election, saying immigration was out of control - a view shared by the RN.
Macron's gamble to call the snap parliamentary election in June backfired, with his centrist coalition losing dozens of seats and no party winning an absolute majority.
The left's New Popular Front alliance came first but Macron ruled out asking them to form a government after other parties said they would immediately vote it down.
Instead, he waited weeks to make his choice.
Even if the political paralysis were to continue despite the appointment of a new government, Macron could not call a new snap election until July next year.
RN MP Sebastien Chenu told BFM TV the far-right party would wait to see what Barnier has to say on immigration, and on changing France's voting system.
MP Laurent Jacobelli, also from the RN, said a condition was that parliament be dissolved as soon as possible, which would be early July.
"The RN wants a prime minister who is committed to dissolving as soon as possible and establishing proportional representation (for parliamentary elections)," Jacobelli told TF1.
Still, the RN was not particularly enthusiastic about Barnier.
"They are taking out of mothballs those who have governed France for 40 years," Jacobelli said
