Hollande said he "notes with respect" Renzi's decision to quit after being defeated in a referendum on constitutional reform in a statement on Monday, going on to praise his "dyanmism and the qualities he put at the service of courageous reforms for his country".
Renzi was "committed to a strong French-Italian relationship" and wanted to "turn Europe to towards growth and employment", the French president said.
Far-right defeat in Austria welcomed
By contrast, Hollande was clearly happy about the victory of former Green Party leader Alexander Van der Bellen in Austria's presidential election.
"The Austrian people has made the choice of Europe and openness" in rejecting the Austrian Freedom Party's (FPÖ) Norbert Hofer, a presidential statement said.
Prime Minister Manuel Valls, who was expected to resign and declare his intention to stand in France's presidential election next year on Monday evening, hailed Van de Bellen's victory in tweet, saying it proved that "populism is not inevitable for Europe".
"Good news for Europe ... Austrians have rejected a far-right president," Foreign Affairs Minister Jean-Marc Ayrault tweeted.That sentiment was not shared by National Front leader Marine Le Pen.
"Congratulations to the FPÖ which fought bravely," she tweeted. "The next electing will be theirs."