The meeting in the so-called four-way “Normandy” format late Thursday lasted more than nine hours, the sources said.
“These were difficult talks in which the different positions and various options for a solution were clearly worked out,” they said.
Participants from all four countries, however, remain committed to the 2015 Minsk peace agreement between Kyiv and Moscow on the separatist conflict, and will “continue to work with vigour on implementing it”, they said.
They have agreed to meet again in March after the next meetings of the so-called Trilateral Contact Group, which includes representatives of Russia, Ukraine and the Organisation for Security and Cooperation in Europe (OSCE).
The Normandy format was launched in 2014 in a bid to bring peace to conflict-torn eastern Ukraine.
Mediation between Russia and Ukraine by Berlin and Paris led to the Minsk agreement of 2015, but Kyiv and Moscow regularly accuse each other of violating its terms.
Tensions have escalated in recent months due to Russian troops massing on the border with Ukraine, with Western governments fearing Russia is planning to invade its neighbour.
According to the French presidency, the discussions Thursday focused on political questions such as whether Ukraine should negotiate with the separatists, as well as humanitarian questions such as the release of prisoners.
“Russia agreed to the substance of the negotiations, but ultimately insisted that… Ukraine negotiate directly with the separatists, which is Ukraine’s only red line,” it said.
“The situation is very tense,” Gabriel Attal, a spokesman for the French government, told Europe 1 radio, but “we are continuing to make progress on the diplomatic front”.