Elected Sunday on a wave of anti-austerity feeling and pledges to put growth at the heart of European economic policy, Hollande attended his first official function Tuesday at a World War II commemoration ceremony.
The Socialist joined his ousted right-wing rival Nicolas Sarkozy in laying a wreath at the Tomb of the Unknown Soldier beneath the Arc de Triomphe in Paris, as France marked the anniversary of the end of World War II in Europe.
Hollande said the ceremony was a sign of French unity after a fierce campaign that highlighted the country's deep left-right divide and saw him win with 51.6 percent of the vote.
"There are issues that unite us all, beyond the person of Nicolas Sarkozy or of me," said Hollande, who is due to formally take office on May 15.
But outside France divisions came to the fore, as Merkel noted in a letter to Hollande that he was assuming power in the European Union's second-largest economy "at a time full of challenges".
"It is up to us to take the necessary decisions for the European Union and the eurozone, to prepare our societies for the future and protect and advance prosperity in a sustainable way," Merkel wrote in the letter released by her office.
Merkel said Monday that she would welcome Hollande with "open arms" when he makes his first foreign trip as president to Berlin next week.
But she also made clear she had no plans to renegotiate the fiscal pact setting tough budgetary rules for EU states that she spearheaded, despite calls by Hollande to rework it to do more to foster growth.
Japan joined those raising concerns about his plans Tuesday, with Finance Minister Jun Azumi warning Hollande to keep France's fiscal discipline in place.
"We want (France) to do what has been decided so far," Azumi told a regular news conference, according to Dow Jones Newswires.
"I don't know whether Mr Hollande will immediately act on what he has said in heated debates during the election campaign.
"But realistically, I think it is impossible (for European nations) to give up on fiscal-rebuilding efforts," he said.
Hollande promised cheering supporters Sunday that he would reopen talks to ensure the EU fiscal pact focused on growth rather than simply imposing deficit-cutting austerity rules.
EU president Herman Van Rompuy announced Tuesday that the bloc's leaders would meet on May 23 for an informal dinner ahead of an EU summit on June 28 and 29 that is expected to focus on growth.
Hollande's transition chief Pierre Moscovici said Tuesday the Socialist would not give up on his plan for "a European project that is more favourable to growth" and that France's partners would budge.
"We will find a compromise. And I am convinced that things are starting well," Moscovici told RTL radio.
The uncertainty generated by Hollande's election and the political turmoil in Greece, where election gains by hard-left and extreme-right parties stripped the ruling coalition of its majority, have riled the markets.
European stock markets slid and the euro fell on Tuesday, with sentiment dominated by uncertainty about the eurozone following the election results in France and particularly Greece.
But Hollande's victory has not yet sparked the financial chaos that Sarkozy warned of during the campaign.
France raised 7.98 billion euros ($9.1 billion) in short-term debt Monday, with lower interest rates paid to investors for two of the three maturities offered.
Hollande plans to replace some of Sarkozy's cost-cutting with higher taxes on the wealthy while balancing the French budget by 2017, despite a hiring spree in education and a return to retirement at 60 for some workers.
After the meeting with Merkel shortly after his inauguration, Hollande will travel to the United States for the G8 summit on May 18 and 19 and a NATO gathering on May 20 and 21.
Hollande's communications director Manuel Valls confirmed Monday that France would use the summit to announce a French troop withdrawal from Afghanistan between now and the end of the year.
Hollande's party must also set off on the campaign trail again in short order for France's June parliamentary elections, when he will hope to secure a ruling majority.