Emmanuel Macron has promised to restore France's global standing, as he was inaugurated as the country's youngest president at the age of 39.
At an elaborate ceremony at the Élysée Palace in Paris, he said his presidency would "give the French back the confidence to believe in themselves".
He vowed to see the EU "reformed and relaunched" during his time in office.
He takes over from François Hollande, whose five-year term was plagued by high unemployment figures.
Mr Macron was proclaimed France's new president a week after his resounding victory over the National Front's Marine le Pen, with 66% of the vote in the run-off poll.
The former investment banker, who had never contested an election before and only formed his centrist movement a year ago, has vowed to shake up the country's political order and reinvigorate its economy.
Tight security was in place across Paris for the ceremony at the president's official residence, with hundreds of extra police on patrol.
France has been under a state of emergency since terror attacks in 2015 and a large section of the city centre was closed to traffic all morning.
'World needs France'
During his inaugural address on Sunday, President Macron pledged to restore the confidence of the French people in their country's future.
"The division and fractures in our society must be overcome," said the centrist politician.
"The world and Europe need more than ever France, and a strong France, which speaks out loudly for freedom and solidarity," he declared.
He said he would convince the people that "the power of France is not declining - that we are on the brink of a great renaissance".
Speaking later during a visit to the capital's town hall, President Macron praised the way Parisians had responded to terror attacks.
He said that rather than hide behind barricades, many had opened their doors and offered help "because the face of Paris is the face of France, that of a living fraternity".
He also promised to strongly support the city's bid to host the 2024 Olympic Games.
He was presented with a chain of office once worn by Napoleon I, as a symbol of his position as Grand Master of the Legion of Honour (a title usually given to the leader of France).
Before the inauguration ceremony began, he spent nearly an hour with his predecessor, who handed him the country's nuclear codes. It was Mr Hollande who launched the new president's political career, appointing him first as adviser and later economy minister.
Despite historic low approval ratings, the former president tweeted after leaving the palace: "I leave a country in a much better state than I found it."
The sunshine president - by Hugh Schofield, BBC News, Paris
It was interesting to note how many "re-" words Emmanuel Macron used in his address. There was "re-formulate", "re-invent", "re-mould", "re-juvenate", "re-launch". And of course "re-naissance".
It was all intended to "re"-enforce the message that this presidency will be one of newness, youth and optimism.
Mr Macron is one of nature's optimists. Francois Hollande - the man from whose hands he took the reins of power - said that when Mr Macron worked for him, he "radiated joy". An almost preternaturally sunny demeanour, combined with his winning way with words, has been the new president's magic formula.
But to hold presidential office is to walk a road of thorns. Rarely is there good news to smile at. Success - if it comes at all - may only be appreciated years later. Mr Macron's "re-splendent" personality is about to tested like never before.
At 39, Mr Macron is France's youngest leader since Napoleon and the first to be born after 1958, when a presidential system was set up.
His En Marche political movement was formed just last year and as a new party - La République En Marche - will be fielding candidates across France in June's parliamentary elections.
He has promised to "work for everyone" and sees his programme as straddling both left and right.
Mr Macron's first week in office will be busy. He heads for Berlin on Monday to meet Chancellor Angela Merkel and to demonstrate his commitment to the European Union.
He is also expected to name a prime minister on Monday morning.
Mr Macron faces major challenges including high unemployment, especially among France's young, and low growth.
He says his main aims are to boost investment and to set up a "new growth model" that increases social mobility and helps the environment.