Abortion and euthanasia are expected to be on the agenda ahead of planned changes to French laws.
It is Mr Hollande's first meeting with the Pope since he was elected in 2012.
Mr Hollande's partner, Valerie Trierweiler, spent a week in hospital after claims emerged he had been having an affair with actress Julie Gayet.
Ms Gayet has announced she is suing Closer magazine, which published the original reports, for breach of privacy.
Ms Trierweiler, meanwhile, is travelling to India on Sunday in support of the work of the French charity Action Against Hunger.
On Thursday she sacked her lawyer for saying she was seeking to end her relationship with Mr Hollande "with the greatest possible dignity".
Ms Trierweiler told the Europe 1 radio network she "felt betrayed".
Hours before Mr Hollande arrived in Rome, a small bomb exploded outside the offices of a French foundation near the Vatican. No-one was injured, police said, but three parked cars were damaged.
In addition to his alleged affair with Ms Gayet, Mr Hollande and Ms Trierweiler have never married - a further irritant to Catholic traditionalists.
Mr Hollande has refused to state whether she remains his official partner and the first lady of France.
The president also has four children with his previous partner, Segolene Royal.
Relations between the Catholic Church and Mr Hollande's Socialist Party have also been strained at a policy level.
The French National Assembly on Tuesday voted to strengthen the right to abortion and is considering a bill on assisted suicide.
When France legalised same-sex marriage in May 2013, tens of thousands of people joined a rally in Paris to express their opposition.
More than 100,000 people have signed a petition drawn up by a Catholic group asking Pope Francis to express to Mr Hollande "the profound malaise and growing concern of many French Catholics".
Ahead of his departure, Mr Hollande said he wanted to discuss Syria and the Middle East peace process with Pope Francis.
Vatican-watchers say the French president wants to reach out to disaffected Catholic voters.
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