A bomb went off in the Rome street where the French-run chuch of Saint-Yves des Bretons is situated, breaking a window in another building and damaging three cars.
Italian police say they are looking into whether the blast is linked to Hollande's visit.
This is his first meeting with the Pope, although he was elected in 2012.
His unmarried status and recent claims that he is having an affair with actress Julie Gayet have also riled Catholic traditionalists.
But Vatican-watchers predict that Pope Francis, who has concentrated on social issues rather than Church doctrine in most of his public statements since becoming pontiff, will raise the "right-to-life" questions that worry much of his flock.
Earlier this moonth Francis denounced abortions as a "frightful" symptom of modern "throw-away" culture and on Wednesday he tweted support for US Catholics taking part in an annual "March for Life" in Washington.
Earlier this month, a group of Catholics mobilised by the anti-gay marriage movement drew up a petition asking Pope Francis to express “the profound malaise and growing concern of many French Catholics” to Hollande when they meet.
More than 100,000 people have signed the petition, which was actively promoted on Catholic social media.