Presidential plane was forced to turn back to Paris and Francois Hollande later completed his journey on a second plane.
During his inauguration speech earlier in the day, Socialist Francois Hollande appealed for “a compromise” over the German-led focus on austerity.
He called for an emphasis on “growth”.
Describing the incident with the first plane, Francois Hollande’s spokesman said that the aircraft “could have been hit by lightning”, the AFP news agency reports.
“For security reasons, it turned back,” he said, adding that no-one was hurt.
It is very common for planes to be hit by lightning and most pilots will experience two strikes a year, some many more.
Planes are designed to dispel the electricity out through the wingtips, so that it is rare to have to turn back after a strike.
Analysts are watching to see how German Chancellor Angela Merkel and Francois Hollande can overcome their differences on how to resolve the crisis.
Stock markets and the euro have fallen amid continuing political uncertainty in Greece.
The chairman of the group of eurozone finance ministers, Jean-Claude Juncker, insisted on Monday that they would do “everything possible” to keep Greece in the euro.
Francois Hollande was sworn in for a five-year term at the Elysee Palace in Paris, becoming France’s first Socialist president in 17 years.
In his inauguration speech, Francois Hollande said he wished to deliver a “message of confidence”.
“My mandate is to bring France back to justice, open up a new path in Europe, contribute to world peace and preserve the planet.”
The new president said he was fully aware of challenges facing France, which he summarized as “huge debt, weak growth, reduced competitiveness, and a Europe that is struggling to emerge from a crisis”.
Francois Hollande also said he wanted other European leaders to sign a pact that “ties the necessary reduction of deficit to the indispensable stimulation of the economy”.
“I will tell them the necessity for our continent is to protect, in an unstable world, not only its values but its interests in the name of commercial exchange,” he added.
After the ceremonies, Francois Hollande named Jean-Marc Ayrault, leader of the Socialist group in parliament, as his prime minister.
Jean-Marc Ayrault, who is regarded as a Germanophile with good contacts in Berlin, had been widely tipped for the post.
Francois Hollande, 57, has spent the past week preparing to take up the presidency, and now the work begins in earnest.
Shortly after his swearing in, Francois Hollande left for Berlin to have dinner with Chancellor Angela Merkel, who said she would welcome the new leader “with open arms”.
But Angela Merkel’s embrace will hide some embarrassment after she openly supported Nicolas Sarkozy in the election battle.
“We don’t think the same on everything,” Francois Hollande acknowledged on French television on Monday.
“We’ll tell each other that so that together we can reach good compromises.”
Francois Hollande has demanded that a European fiscal pact that cracked down on overspending be renegotiated to include a greater emphasis on measures to stimulate growth, while Germany insists the treaty must be respected.
Whatever their differences, the crisis in the eurozone will put them under huge pressure to compromise, our correspondent says.
As the eurozone’s two biggest economies – and biggest contributors to its bailout funds – Germany and France are key decision-makers over the strategy supposed to pull Europe out of crisis.
According to official figures released on Tuesday morning, the French economy showed no growth in the first quarter of 2012. Growth in the final quarter of 2011 was also revised down to 0.1% from 0.2%.
However, Germany’s economy grew by a stronger than expected 0.5% in the first three months of the year.
Following his German trip, Francois Hollande will hold his first cabinet meeting on Thursday followed by a visit to Washington to meet US President Barack Obama on Friday.
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