Macron is on an official visit to Italy, and thanked outgoing PM Mario Draghi before meeting Meloni.
Macron, who's currently on an official visit to Italy, wrote on Twitter that the two countries had to continue to work together "with dialogue and ambition."
Macron and Meloni discussed current European issues including the need to provide quick and common answers to increased energy prices, support for Ukraine and the management of migrant flows, Italy's prime minister's office said in a statement.
Before posting a picture of his meeting with Meloni, Macron posted a picture of outgoing Italian PM Mario Draghi, writing simply "Grazie Mario."
Meloni, Italy's first woman prime minister, formally took over from Draghi as head of government earlier on Sunday after she and her new cabinet team were officially sworn in on Saturday in Rome, giving the country its most right-wing government since World War Two.
Meloni's Brothers of Italy party has neo-fascist roots, but she sought to project a moderate image during the election campaign, dropping previous anti-EU rhetoric and pledging to keep Italy at the heart of European and Western institutions.
European Commission leaders in Brussels sent her messages of congratulations on Saturday.
Macron, who on Sunday attended a conference in Rome aimed at seeking ways to promote world peace, will meet Pope Francis on Monday.