Hollande described Trump's statements as "unacceptable", and German Chancellor Angela Merkel called on the EU to press ahead with its own plans whatever the US says.
EU leaders have been rattled by Trump's comments on Europe and the NATO transatlantic alliance. He has voiced his support for Britain's departure from the EU, criticized European refugee policies and called NATO "obsolete".
Hollande hit out at Trump as he arrived at the informal summit on the future of the EU in Malta. "There are threats, there are challenges. What is at stake is the very future of the European Union," he said.
"It is unacceptable that there should be, through a number of statements by the US President, pressure on what Europe should be or what it should no longer be."
Merkel called on fellow EU leaders to unite, as she arrived for the summit in Valletta, Malta's capital. "I already said that Europe has its destiny in its own hands. And I believe the stronger we state clearly how we define our role in the world, the better we can take care with our transatlantic relations," she said.
Austrian Chancellor Christian Kern criticized Trump's ban on travel from seven Muslim-majority countries as "highly problematic." He blamed some of the migration problems on US intervention in the Middle East. "There is no doubt that America shares responsibility for the refugee flows by the way how it intervened militarily," he said, according to AFP.
Concerns about Trump's 'decisions and attitudes'
The concerns about Trump continued into the discussions. Malta's Prime Minister Joseph Muscat said EU leaders expressed concern about some "decisions and attitudes" of the Trump administration during their deliberations at the summit.
"Obviously there was concern among the EU 28 on some decisions that are being taken by the new US administration and some attitudes that are being adopted by the said administration. Nevertheless there was no sense of anti-Americanism. There was a sense that we need to engage with the United States just the same, but we need to show that we cannot stay silent where there are principles involved."
The President of the European Council, Donald Tusk, said protecting Europe's "unique" relationship with the United States was still the "highest political priority" for not just the EU, but for all of Europe. Speaking at a press conference at the Malta summit, Tusk said that transatlantic cooperation "has until now been a key pillar of the free world."
His remarks were markedly more conciliatory than earlier int he week, when he called the Trump administration an "external threat to Europe."
Potential EU envoy 'hostile'
The criticism of Trump came after it was revealed that the European Parliament's main political party is attempting to block Trump's expected choice for US ambassador to the European Union.
A letter from the Group of the European People's Party, or EPP, urges the EU to reject US businessman Ted Malloch, calling him "hostile and malevolent" and accusing him of "denigrating the EU."
"In these statements, the prospective nominee expressed his ambitions 'to tame the bloc
like he brought down the Soviet Union,' eloquently supported dissolution of the European Union and explicitly bet on the demise of the common currency within months," they say in the letter to the presidents of the European Council and European Commission.
"We are strongly convinced that persons seeing as their mission to disrupt or dissolve the EU, should not be accredited as official representatives to the EU."
The letter ends by urging EU leaders Donald Tusk and Jean-Claude Juncker not to accept Malloch should he be Trump's pick. Envoys to the EU must be approved by the European Council, the European Commission and signed off by EU leaders.
Following her trip last week to Washington, UK Prime Minister Theresa May was expected to brief EU leaders on her meeting with Trump in which she received assurances that he is fully committed to NATO. She will call on other members of the EU to increase their defense spending
Britain's future relationship with the EU is also on the agenda in Malta.
May wants to invoke Article 50 by the end of March, firing the starting gun on a two-year divorce wrangle.
The UK government has stressed it wants to see a strong and successful European Union after Brexit.
In Malta, May is already an outsider, invited to some meetings but not all. She won't join the other EU leaders when they discuss recent comments by Tusk, the European Council president, calling Trump a "threat" to the European order