President Trump spent two days with Emmanuel Macron on an official visit to France, where he was guest of honour at Bastille Day celebrations in Paris.
Mr Macron said of Mr Trump in an interview with the Journal du dimanche newspaper on Sunday: "Our countries are friends, so we should be too.”
The new French president said Mr Trump "understood the meaning of my approach, including the link between global warming and terrorism, and he told me he would try to find a solution”.
He added: "We talked in detail about what would allow him to come back to the Paris agreement.”
The 39-year-old said he was optimistic that "something can happen” on the American position on the Paris Climate Agreement, after the country pulled out earlier this year.
He said: "Donald Trump listened to me.”
During the interview, he said he had started to build a relationship of trust with the US leader and give the Americans a strong image of France.
He said: "I think Donald Trump left with a better image of France than when he arrived.”
He also said the two leaders gained a "better, intimate knowledge of each other”.
During the official visit, the two presidents discussed General Pershing, who was the leader of the American troops in France in 1917.
He said: "It was important to see that our two nations have strong human and civilisational ties.
"It is important to maintain the dialogue so that the United States can eventually return to the field of action against global warming and play the game of multilateralism.”
Mr Macron avoided the subject of the relationship between the United States and Russia during the interview.
Speaking of his relationship with the German Chancellor, he said: "With Angela Merkel, I have a very direct, frank, friendly and permanent dialogue.”