An embattled Hollande shook hands with a glum-looking Pope Francis at the start of the private audience, and a high-ranking prelate said he expected that there would be "no holds barred" in their conversation.
The Vatican said in a statement after the talks that the two discussed "constructive cooperation for the common good", as well as issues including "family, bioethics and the respect of religious communities".
Hollande said he and Pope Francis had the "same concern" about the status of Christian minorities in the Middle East and he hailed the Pope's "radiant personality".
He also said he had asked the Pope for the Vatican to receive Syria's main opposition group, the Syrian National Coalition, as the first talks between Syria's warring sides in Switzerland got off to a rough start.
"The Geneva II conference should be aimed at transition. We need to do everything to stop the fighting and dispatch humanitarian aid," Hollande said.
Hollande has previously said that the Pope, a "great moral authority", could help "find a political solution" to Syria's devastating civil war.
Security measures for Hollande's visit were stepped up following the explosion just hours before of a small bomb packed with nails and lead pellets, which damaged cars and smashed windows near a French church in Rome.
"There has been no claim of responsibility," a police spokesman said.
Residents in the area said they thought the blast may in fact be linked to a nearby nightclub that they said had mafia ties.
Police bomb disposal experts were called out again later on Friday after receiving an anonymous phone call about a bomb placed under the famous colonnade on St Peter's Square, which turned out to be a false alarm.
In Paris meanwhile an aide to French First Lady Valerie Trierweiler said she would be pressing ahead with a planned visit to India this weekend for a charity effort, although her official status is now unclear.
Trierweiler, 48, has been holed up in a presidential residence in Versailles near Paris following a week-long stay in hospital after revelations about Hollande's tryst with 41-year-old actress Julie Gayet.
Hollande has promised to clarify his partner Trierweiler's official status before his state visit to Washington on February 11th. The story has overshadowed Hollande's Vatican visit.
'Difficult time in his private life'
The French president, already plagued by low popularity due to the economic crisis, hopes to reconcile with a Catholic electorate largely hostile to his policies.
Hollande sees the visit as a chance to send "a strong message of dialogue and attention to the Catholics", an advisor said at a briefing ahead of the trip.
But he admitted: "Hollande's trip has clearly come at a difficult time in his private life".
Hollande may be hoping some of the Pope's popularity rubs off on him and, despite clear differences on moral issues, there is common ground on international affairs.
His diplomatic overture will be made no easier by lawmakers' decision this week to greenlight a change in the country's abortion laws, effectively making it easier for a woman to terminate a pregnancy.
Anger among staunch Catholics has also been fuelled by plans for the legalization of assisted suicide - with French bishops speaking out to condemn a topic Hollande promised to support in his electoral campaign.
Relations between part of the electorate and the government soured notably last year when France legalized gay weddings, despite hundreds of thousands of people taking to the streets to hold huge protests.
Some 110,000 frustrated Catholics have signed a petition calling on the congenial Pope Francis to get tough and raise their concerns with Hollande.
Although the Pope, 77, has called for "mercy" toward gays, divorced people and women who have abortions, Vatican experts say Pope Francis is a conservative at heart.
He has denounced abortions as a "frightful" symptom of today's "throw-away culture", and on Wednesday he tweeted his support for US Catholics taking part in the annual anti-abortion "March for Life" in Washington.
The Vatican said Hollande and Francis had also discussed international issues including poverty, development, immigration and the environment.