A Vatican statement said Francois Hollande and Pope Francis’ talks covered the family, bioethics and respect for religious communities.
France is planning to amend its laws on abortion and assisted suicide.
Francois Hollande’s partner, Valerie Trierweiler, spent a week in hospital amid claims he had been having an affair with Julie Gayet.
Julie Gayet has announced she is suing Closer magazine, which published the original reports, for breach of privacy.
Valerie 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 withFrancois Hollande “with the greatest possible dignity”.
Valerie Trierweiler told the Europe 1 radio network she “felt betrayed”.
Speaking after their meeting, Francois Hollande said he had asked the Pope if the Vatican would receive a delegation from one of Syria’s main opposition groups, the National Council.
Talks aimed at ending the three-year-old Syrian conflict are under way in Switzerland.
“We need to do everything to stop the fighting and dispatch humanitarian aid,” Francois Hollande said.
Hours before Francois 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 Julie Gayet, Francois Hollande and Valerie Trierweiler have never married – a further irritant to Catholic traditionalists.
Francois Hollande has refused to state whether Valerie Trierweiler remains his official partner and the first lady of France. The president has promised to clarify the situation before he makes a state visit to Washington next month.
He also has four children with his previous partner, Segolene Royal.
Relations between the Catholic Church and Francois 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.
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