Hollande highlighted trade and diplomacy in global conflicts as areas for concern.
"There are challenges posed by the new US administration, in regards to commercial rules, in regards to the conflicts in the world," he said in Berlin.
"We of course have to speak to Donald Trump, as he was chosen by the Americans to be their president.
"But we have to do it with a European point of view and promote our interests and values. That's why it's so important not only to talk to each other but also to come together."
Terror threat, rise of populism
Both leaders focused on the need for unity as Europe faces a changed global political landscape, unsettled by terrorism, Trump's election and Britain's impending exit from the European Union.
"The European Union is facing huge internal and external challenges, which we are both convinced we can only manage together," Merkel said as she appealed for solidarity among its members.
"We can see that the global framework is challenging rapidly, and we have to face these challenges."
Hollande highlighted the test to European values with the rise of populism.
"Europe doesn't not only face external threats but also internal," he said, citing "the rise of extremists who use external factors to create internal disruption."
Hollande and Merkel spoke before paying a visit together
Friday to the Berlin square where a terror attacker drove a truck
into a Christmas market, killing 12 people.
"We are facing the Islamist terror threat together, and we want to make clear that we will not let anyone take away the way we live," Merkel said.
White House meeting for Trump and May
The meeting between Merkel and Hollande came shortly before UK Prime Minister Theresa May met with US President Donald Trump
at the White House in what was the latter's first meeting with a foreign leader since assuming office a week ago.
Trump said he is open to a warmer relationship with Russia and believes torture works as an interrogation technique. May, who was under pressure from rights groups in Britain to condemn torture during her visit, said only that on areas of disagreement, she would carry out a "open and frank discussion" with the US leader.
Merkel and Hollande's remarks, made after a working breakfast together, came ahead of an EU summit next week in Malta, which currently holds the rotating EU presidency.
EU members are grappling with the prospect of Britain's exit from the European Union, with negotiations set to begin after Britain triggers Article 50
of the Lisbon Treaty -- the legal mechanism through which Brexit officially begins. May wants this to happen by the end of March.
France and Germany will hold elections later this year. Hollande, who has governed since 2012, announced he would not run for re-election amid dismal approval ratings. Merkel, however, will seek her fourth term in office.
A number of populist parties with anti-EU, anti-immigration agendas hope to get a boost from Trump's election in the United States and his populist message.