Thousands of people demonstrated across France on Saturday against Emmanuel Macron's decision to pick centre-right politician Michel Barnier as prime minister, with leftist parties accusing the president of ignoring election results.

Macron named 73-year-old Barnier, a conservative and the former Brexit negotiator for the European Union, as prime minister on Thursday, capping a two-month search following his ill-fated decision to call a legislative election that delivered a hung parliament.

"Democracy is not only the art of knowing how to accept victory, but the humility to accept defeat," Jean-Luc Melenchon, head of the far-left France Unbowed party (LFI), told protesters at the start of the march in eastern Paris.

"I call on you to undertake a long battle."