"Our allies had evidence that chemical weapons had been used, and we had proof that these weapons could be attributed to the Syrian regime, which led us to conduct this intervention", Macron added.
"I assure you, we have convinced him that it is necessary to stay for the long-term", Macron told veteran journalists Jean-Jacques Bourdin and Edwy Plenel.
The statement came hours after French President Emmanuel Macron asserted that Paris had convinced Trump to stay engaged in Syria "for the long-term".
However, Mr Macron said that by joining forces with France and the United Kingdom for last Saturday's air strikes, the USA "fully realised that our responsibility went above and beyond the war against IS, and that it was a humanitarian responsibility as well on the ground".
He reaffirmed that there was proof of chemical attacks, adding: "We had reached a point where these strikes were necessary to give back the (international) community some credibility".
"It was retaliation, not an act of war", Macron said in justifying the operation a day before the French parliament was set to debate it.
British Prime Minister Theresa May said in London that the West had tried "every possible" diplomatic means to stop Assad from using chemical weapons.
At a meeting of the Organisation for the Prohibition of Chemical Weapons (OPCW), UK representative Peter Wilson said: "Russia has argued that the attack on Douma was somehow staged, or faked".
He said France now wants to involve Western powers, Russian Federation and Turkey in a new diplomatic initiative to find a sustainable political solution in Syria.
On Friday, Trump said that the USA is "prepared to sustain this response until the Syrian regime stops its use of prohibited chemical agents".
Macron had warmer words for Turkey.
Meanwhile, leader of the far-right party Front National Marine Le Pen said with its decision to follow the U.S. and Britain to carry out the strikes, France lost "an opportunity to appear in the global scene as an independent power". "With those strikes we have separated the Russians and the Turks on this".
On Friday, the United States, France and the United Kingdom launched a series of strikes on a research laboratory and two storage facilities associated with Syria's chemical weapons program.
"These strikes against Syria engage us in a way with unpredictable and potentially dramatic consequences", she warned on Twitter.
Both Putin and Rouhani agreed the missiles strikes had "seriously damaged" the prospect for a political settlement in Syria, the statement said.