Bayrou has "tried to find new balances", he states in a letter to concerned politicians ahead of the announcement of the new ministers, reports media company BFMTV.
Many names in the new government are well-known in French politics.
Former Interior Minister Gérald Darmanin becomes Justice Minister, while Defense Minister Sébastien Lecornu remains in his post, as does Foreign Minister Jean-Noël Barrot. Interior Minister Bruno Retailleau also retains his position.
Changed his mind about Bertrand
Éric Lombard goes from being CEO of the French state financial institution Caisse des dépôts to becoming Finance Minister – a difficult position given France's high budget deficit, which stood at 6.1 percent of GDP at the beginning of December.
The Education Minister will be France's former Prime Minister Élisabeth Borne.
Former Prime Minister Manuel Valls, from the Socialist Party, will also get a ministerial position responsible for France's overseas territories.
Most of those in key positions, however, belong to the same centrist alliance as President Emmanuel Macron and Bayrou.
Earlier on Monday, right-wing conservative Xavier Bertrand made a statement that he had been offered the post of Justice Minister over the weekend, but that the offer had been withdrawn in the morning due to Bertrand's opposition to the far-right party National Rally.
In the statement, published on X, he writes that he "refuses to participate in a French government formed with the approval of Marine Le Pen."
Already threatened with no-confidence
The previous government fell at the beginning of December after a no-confidence vote. This followed criticism of then-Prime Minister Michel Barnier's forcing through a budget for social security with an exception rule, as he did not have sufficient support in parliament.
Hard-left politician Jean-Luc Mélenchon, from the party Unsubmissive France, which President Emmanuel Macron has ruled out talks with, has already announced plans to table a no-confidence motion in parliament in January.
