France's newly appointed Prime Minister Michel Barnier faced the first serious test of his authority on Tuesday, when he gave a speech outlining the plans, most specifically related to tax and the budget, of the country's new government.

French President Emmanuel Macron's decision on calling a snap general election in the summer to see off the challenge of the far-right National Rally party, or RN, led to months of political stalemate that only ended a few weeks ago with the formation of a new minority government headed by Barnier, but with plenty of powerful opponents.

It is under pressure to find tax increases and spending cuts in order to come up with a budget for next year that can be presented to lawmakers for their approval by the middle of this month.

Barnier is well aware that there are rivals on both the political left and right who will be quick to try and bring the government down.

"I have been here for 20 days and I do not know for how much longer," Barnier said at the weekend. "But I am here as someone who is embarking on a long journey ... with a lot of determination."

Figures published by the French statistics office INSEE at the end of September revealed that the country's borrowing in the second quarter of the year had reached 68.9 billion euros ($76.4 billion), meaning that between April and June, public debt rose to 112 percent of the GDP.

At the end of May 2024, Standard & Poor downgraded France's creditworthiness for the first time since 2013.

Daily newspaper Le Parisien said it was expected that Barnier would use tax measures to try and increase state revenues by 15 billion to 18 billion euros, with the paper saying he would "propose several levers to achieve this objective", including raising corporation taxes, a levy on energy companies, and taxes focusing on, in his words, "those who can contribute to this effort" and sparing "those who are on the ground, who work, who produce".

But Gerald Darmanin, a former government minister from Macron's centrist Renaissance party, said tax increases could prove hard to swallow.

"Many of us will not be able to support a government that would increase taxes: that would go against everything positive that we have done for the French people," he said.

RN came out of the summer's National Assembly elections with the largest share of seats of any party, but no majority, and will have a significant say over the fate of Barnier's government.

Given the growing success of right-wing parties across Europe, there will also be great attention paid to Barnier's proposals on immigration.

Already a volatile political issue in France, it has come to the fore again following the recent murder of a university student near Paris, with the Agence France Presse news agency reporting that the suspect arrested was a Moroccan national who had been the subject of an order to leave France because of previous offenses.