Like most world leaders, with the exception of Russia's Vladimir Putin, Hollande was slow to congratulate Trump.
But shortly before midday the Elysée presidential palace did so in a tweet and the president made a statement on television.
He congratulated the victorious Republican "as is natural between two heads of democratic states" but went on to warn of a "period of uncertainty" and expressed sympathy for defeated Democrat candidate Hillary Clinton.
"What is in the balance is peace, it is the struggle against terrorism, it's the situation in the Middle East, it is economic relations and it is the preservation of the planet," Hollande said.
Far right delighted
National Front (FN) leader Marine Le Pen tweeted congratulations to Trump and "the free American people" even before the victory was announced and, despite falling out with his daughter, her father, Jean-Marie Le Pen, declared "Today the United States, tomorrow France!".
"It's a very difficult year for the oligarchy," FN vice-president Florian Philippot said, recalling the UK's Brexit vote and predicting that, "if Mr Trump keeps his promises", the Trans-Atlantic Free Trade Agreement is "dead and buried".
Like Trump, the FN is anti-globalisation and presents itself as an outsider that has been pilloried by the establishment.
The FN, which has received a nine-million-euro loan from a Russian bank, believes that France should accept the Kremlin's annexation of the Crimea from Ukraine and Philippot said that Trump's election means that "perhaps we have avoided a war with Russia, perhaps we will move towards a form of appeasement".
Mainstream right fears 'populism'
Former prime minister Jean-Pierre Raffarin also scented the chance of an FN victory in 2017, although for him it should be a wake-up call to the mainstream right Republicans.
"The principal news for us French is that Marine Le Pen can win in France," Raffarin, who is backing former prime minister Alain Juppé in the Republicans primary, warned. "This means that extreme populism can win."
In a statement Juppé called for France and Europe to "defend their interests in dialogue with the US administration" and warned the French of 'the dangers that demagogy and extremism constitute for democracy and the vital character of the choices they have to make".
Juppé has called for "diversity in unity", clashing with his main rival, former president Nicolas Sarkozy, over attitudes to Islam in France.
His campaign manager, Gilles Boyer, took a swipe at Sarkozy's proposal to drop halal food options from school canteen menus, tweeting "Double French fries please" and "The moral: you have to vote".
Sarkozy said the American people had rejected establishment thinking that "forbids any debate on the dangers that face our nation", citing unfair world trade, immigration and terrorism as key concerns.
Another would-be Republicans presidential candidate, Bruno Le Maire, claimed the US result vindicates his plan to weaken France's major trade unions and reform the country's administration.
"Faced with populisms, in the US and in France, if we put up the same people populism will win," he told Radio Classique.
Jean-Frédéric Poisson, a member of the small Christian Democrat Party who is also standing in the mainstream right primary, enthusiastically congratulated Trump.
"After #Brexit new victory for the voters against the system," he tweeted.
Socialists call for unity against FN
France's ruling Socialist Party responded with calls to the hard left not to stand candidates against it in the first round of the 2017 election.
"The left has been warned!" the party's national secretary Jean-Christophe Cambadélis tweeted. "If we continue with our irresponsible childishness it will be Marine Le Pen."
Foreign Affairs Minister Jean-Marc Ayrault said that Paris will exercise "vigilance" in defending its interests.
Judging that "what he has said up until now raise a number of concerns", Ayrault said, "We are in an uncertain world, in a dangerous world even, which is going through major changes."
"What will happen to the Paris climate change accord, to the Iranian nuclear agreement, which Donald Trump wants to challenge?" he asked.
Environment Minister Ségolène Royal insisted that Trump cannot pull out of the Cop21 agreement because countries have signed up for a minimum of three years plus a year's notice.
The American electoral campaign was not a "beautiful spectacle for democracy", she judged. "We have to be very careful to respect the voters' intelligence and bring them to positive votes and not votes of fear."
Hard left believes Sanders would have won
On the hard left, presidential candidate Jean-Luc Mélenchon said that the result showed that the US Democrats had chosen the wrong candidate.
"[Bernie] Sanders would have won," he commented. "The primaries were a machine for muzzling the people's energy. Now let's quickly get off the Atlanticist runaway train."
Left-wing Socialist Benoît Hamon, who is standing in the Socialists' primary, agreed that Sanders would have won and called for policies that appeal to the people.
To read our coverage of this year's US presidential election click here