A statement from Sarkozy's office said the French president underlined to Abbas the urgency of a resumption of the Middle East peace process.
Sarkozy appeared to be positioning himself as a Middle East peace mediator. He called Abbas on Thursday after meeting Netanyahu the night before.
The statement said Sarkozy laid out in light of his recent international contacts the conditions that would allow a quick return to the talks. The statement did not say what those conditions would be.
An Abbas aide, however, told AFP that Sarkozy made "important suggestions" during a phone conversation with Abbas.
"President Sarkozy had very important suggestions on how to move the peace process forward," Nabil Abu Rudeina told the French news agency.
He did not elaborate, but reportedly said Sarkozy had shared details of his meeting with Netanyahu and the two agreed to talk again in a few days.
Another senior Palestinian official was quoted as telling AFP on condition of anonymity that among the topics discussed was the idea of organizing a Middle East peace conference in Moscow, an idea Russia has been pushing for months.
During a speech in Ramallah on Wednesday, Abbas reiterated his position that negotiations will not be resumed as long as settlement construction is not halted entirely.
He also recapped the principles that will guide the Palestinians during negotiations: a Palestinian state within the 1967 borders, Jerusalem as its capital, the release of prisoners, and the right of return for refugees in line with the United Nations Resolution 194.
Following Netanyahu's meeting with Sarkozy on Wednesday, the two leaders said in a joint statement that they agreed to make every effort to revive the peace process.