Macron met Netanyahu one-on-one after the two attended Sunday's commemoration of the wartime Vél d'Hiv roundup of Jews.
Following the meeting, Macron declared that France "stands ready to support all diplomatic efforts" in favour of the two-state solution, under which Israel and Palestine "should live side by side behind secure and recognised borders, with Jerusalem as the capital".
Israel and the Palestinians have not met since the failure of a US mediation effort in 2014.
Macron also pointed out that the continued construction of Jewish settlements in the Palestinian territories is against international law, a point he made to Palestinian President Mahmud Abbas when he visited Paris at the beginning of the month.
During the French presidential election campaign Macron had little to say on the Middle East but did oppose the idea of France recognising a Palestinian state without an agreement with Israel.
Iran nuclear deal
The French president's other statements may have been more to the Israeli prime minister's liking.
Macron promised "vigilance" in ensuring that Iran respects the accord on nuclear technology reached with Western powers, including France.
He also said he "shares Israel's concern about the arming of Hezbollah", the Lebanese Shia-Muslim movement that has combatted Israeli invasions of the country and is currently fighting alongside President Bashar al-Assad's forces in Syria.
Anti-Zionism and anti-Semitism
The invitation to the Vél d'Hiv ceremony, where Macron at one point addressed Netanyahu as "Dear Bibi", was the first to an Israeli prime minister, delighting the guest but angering some of his French Jewish critics.
In a speech that accepted French responsibility for the roundup of Jews who were sent to Nazi concentration camps, Macron promised to fight alongside Israel against "dark terrorism and the worst of fanaticisms" and declared "We will cede nothing to the messages of hate, to anti-Zionism because it is the reinvented form of Zionism."
After their meeting, Netanyahu hailed his host's "determination" to fight racism and anti-Semitism and said France had "enormous potential" under the leadership of its new president.
Left-wing French MP Clémentine Autain on Monday dubbed the invitation to Netanyahu "particularly strange".
"Benjamin Netanyahu is a man of the right, of the extreme right," she told RFI. "This is a man who has established a strategy of reinforced settlement and who is certainly not the man who will allow the realisation of a peace agreement in that region."
Netanyahu faces more controversy in Hungary
The Israeli prime minister left for Hungary on Monday.
His visit there has already aroused concern within the 100,000-strong Jewish community there, many of whose members have accused Viktor Orban's right-wing government of exploiting anti-Semitism in a campaign against millionaire philanthropist George Soros, whom it accuses of campaigning in favour of immigration.