On Thursday, a gunman killed a police officer and wounded two others on Paris' iconic Champs-Elysees boulevard before he was fatally shot.
Speaking at the White House after a terrorist attack on Paris last week left a policeman dead, Mr Trump said she was "strongest on borders, and she's the strongest on what's been going on in France".
It's the first time in living memory a presidential election is taking place during a state of emergency, which was put in place after the Paris attacks of November 2015.
Nine candidates will be eliminated in today's vote in the highly-charged election, with François Fillon, Benoît Hamon, Marine Le Pen, Emmanuel Macron and Jean-Luc Mélenchon considered the frontrunners.
Almost 47 million people are eligible to vote and most polling stations will close at 5 p.m. GMT (8 p.m.in Israel) with those in major cities shutting an hour later.
Unpopular incumbent President Francois Hollande made the unusual move previous year of pledging to not stand for re-election.
The vote "is really important, mainly because we really need a change in this country with all the difficulties we are facing and terrorism", said Paris resident Alain Richaud, who was waiting to cast his vote.
Voter Marie-Christine Colrat said: "Listen, too many candidates. And candidates that caused us a lot of problems, I think that's not a good thing for France". Those in the largest cities will close at 8 p.m. (1800 GMT).
The sun glistened across most of France as voters - and candidates - cast their ballots.
The turnout figure at 5pm in France (midnight in Thailand) was estimated at 69%, slightly below the 2012 election turnout, according to France's Interior Ministry.
Analysts point out that the latest attack in Paris, which killed a police officer and left three other people wounded Thursday, may have contributed to her surge in support, though some survivors of these and other attacks view her as a fear monger.
France's 10 per cent unemployment, its lacklustre economy and security issues topped concerns for the country's 47 million eligible voters.
Harry Kane: Tottenham want to win Premier League for Ugo Ehiogu
Hazard, arguably the best player in the Premier League this season, said he knew why Conte left him out of the XI. "If you compare our team with Tottenham's, (Spurs boss Mauricio) Pochettino has worked for three years".
In early vote-counting, Macron, a 39-year-old independent, has 23.8% of the vote at of 1am Thailand time, while the National Front's Le Pen, 48, has 21.6%. Melenchon says that's a possibility if he can't renegotiate France's role in a bloc blamed for myriad economic and security woes.
A French exit of either would be far worse than Britain's - it could spell death for the EU, the euro and the whole idea of European unity borne from the blood of World War II.
If Le Pen or Melenchon win a spot in the summer's runoff, it will be seen as a victory for the rising wave of populism reflected by the votes for Donald Trump and Brexit. Both candidates have tapped into widespread disillusionment with traditional parties.
Current polling for the second round projects Macron will win with a comfortable margin against Le Pen, but 2016 has offered us a fair amount of skepticism for polls.
This year's Socialist party presidential candidate Benoit Hamon cast his ballot in Trappes, a Paris suburb.
French presidential candidate Emmanuel Macron (L) casts his ballot at a polling station in Le Touquet on April 23, 2017. "It's a disaster. I am going to go and vote but only because I have to", said 60-year-old Pierrette Prevot in Paris. Fake jobs scandal Closely watched around the world, the French campaign has been full of twists and turns.
France has spoken, for now. The country voted yesterday in the first round of its presidential elections, after weeks of campaigning that have been dogged by scandals, gaffes and surprises.
Dozens of people lined up to vote Sunday inside the French Embassy in Cairo, where many expats work for French companies and schools.
Polls now suggest Le Pen will have a hard time convincing enough voters to join her in the second round.
Polls opened in France's far-flung overseas territories but voting wouldn't start until Sunday on the French mainland. "Candidates who want fewer security measures, who want to reduce the police's powers, have not got my vote", Belkechout told AFP.
French citizens lined up to vote at Montreal's only polling station at Stanislas College in Outremont.
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