France and Europe risk being dominated, crushed and marginalised if they do nothing to counter the policies of Donald Trump, French Prime Minister Francois Bayrou said on Monday before the new US president's inauguration.

"The United States, with the inauguration of the president, has decided on a politics that is incredibly dominating," Bayrou said in the southwestern city of Pau where he is mayor, pointing to the incoming administration's policies on the dollar, industry and investment.

"If we do nothing then our fate will be simple. We will be dominated, we will be crushed, we will be marginalised. It is up to us, French and Europeans, as it is impossible without Europe," he added.

Trump's inauguration "puts us face-to-face with our responsibility", he added, also evoking "the power of China".

French President Emmanuel Macron had even before Trump's election for a second term emphasised the importance of Europe gaining a "strategic autonomy" by limiting its dependence on the United States, particularly in defence.

Named by Macron late last year as premier to end a half year political crisis, Bayrou, a veteran centrist long known to have coveted the post of premier, is taking an increasingly assertive stance both in foreign and domestic policy.

Trump is later on Monday due to be sworn in for a historic second term, promising a new "golden age" for the United States as the world braces for a return of his unpredictable leadership.

The most prominent French political figures invited to the inauguration are the leader of the extreme-right Reconquete! (Reconquest!) party, Eric Zemmour, who won seven per cent of the vote in 2022 presidential elections, and its MEP Sarah Knafo who is also his partner.