Francois Hollande, the country's first socialist president in 17 years, was sworn in at an inauguration on Tuesday.
Outgoing president Nicolas Sarkozy was farewelled by crowds outside the Elysee Palace in Paris, which will be Mr Hollande's new residence.
In his first speech as president, he said he recognised the challenges ahead.
The new president has vowed to rework a deal on government debt and has been emphasising growth in Europe and stimulus for the French economy.
However, he is already on his way to Berlin to meet German Chancellor Angela Merkel who is insisting on austerity measures and repayment of debt.
Mr Hollande will appoint a German-speaker as prime minister and an experienced moderate as finance minister this week.
The moves are meant to send reassuring signals on his plans for relations with Berlin and cutting the country's deficit.
Jean-Marc Ayrault is widely-tipped to be named premier as he has strong contacts with the Berlin establishment.
Mr Hollande is expected to name Michel Sapin as finance minister, a post he held two decades ago.
He may also name Pierre Moscovici, who ran Hollande's election campaign and is a former minister for Europe, to an enlarged European Affairs ministry.