In his first speech as president, Macron said his main priority would be "to give back to the French people the confidence that for too long has been flagging".
"I will convince our compatriots that France's power is not in decline, but that we are at the dawn of an extraordinary renaissance because we have all the qualities which will make ... the great powers of the 21st century," he said.
While France's place was in the European Union, the 28-member bloc needed to be "reformed and relaunched", the new president said.
Macron assumed power after an hour-long private meeting with Hollande in which official access to France's nuclear missile launch codes was handed over.
After the formalities, a 21-gun salute rang out from the Invalides military hospital on the other side of the River Seine.
|Macron met with predecessor Hollande before the ceremony to discuss the most sensitive issues facing France, including the country's nuclear codes [Yoan Valat/AP]|
Later, the new president paid tribute at the Tomb of the Unknown Soldier beneath the Arc de Triomphe, where he stood in a downpour, without a raincoat or umbrella, to light the flame in honour of France's war dead.
He went on to shake hands with supporters along the Champs Elysees, who were taking selfies and waving French tricolour flags, amid tight security.
Some 1,500 police officers were deployed near the presidential palace and on the Champs Elysees.
Macron faces a host of daunting challenges, including tackling stubbornly high unemployment, fighting violence and healing divisions exposed by an often vicious election campaign.
Some analysts and opponents have questioned the strength of his mandate; though Macron defeated his rival Marine Le Pen in a landslide, many who voted for him on May 7 said they cast their ballot reluctantly, in a bid to boot out the far right.
|Macron lights the flame during a ceremony at the Tomb of the Unknown Soldier at the Arc de Triomphe in Paris [Alain Jocard/Reuters]|
Macron vowed to glue France together, saying,"The time has come for France to meet the challenges of our time."
"The divisions and fractures that run through our society must be overcome, whether they be economic, social, political or moral.
"I can assure you I didn't think for a single second that (the confidence) was restored as if by magic on the evening of May 7. It will be slow, demanding but essential work."
He added: "France is strong only if she is prosperous."
A convinced European integrationist unlike Le Pen and other candidates, he went on: "The world and Europe need France now more than ever and they need a strong France with a sense of its own destiny."
He pledged to press for reforms to the EU, saying: "We will need a more efficient Europe, a more democratic Europe, a more political Europe because it's the instrument of our power and our sovereignty, I will work on that.
"The world needs what French men and women have always taught it: the audacity of freedom, the demand for equality and the desire for fraternity," he said.
|Macron greets supporters after a ceremony at the Arc of Triomphe following his formal inauguration ceremony as French President [Alain Jocard/AP]|
Source: News agencies