French Foreign Minister Jean-Yves Le Drian called for easing tensions with Russia as top French ministers met their counterparts in Moscow on Monday.
"The time has come, the time is right, to work towards reducing distrust," Le Drian said at a press conference in the Russian capital.
Le Drian and Defence Minister Florence Parly held the first meeting in the so-called "2+2" format suspended after Russia seized Crimea from Ukraine in 2014.
"We have come to suggest, in the name of the president of the republic, a new agenda of trust and security," Le Drian said.
Parly said "it is important to talk to each other, to avoid misunderstanding and friction."
Russian Foreign Minister Sergei Lavrov said progress on rebuilding ties was "possible and necessary".
Ties between Russia and Europe have been deeply strained since 2014, when the European Union and United States imposed sanctions over the annexation of Crimea and Moscow's support for separatists in eastern Ukraine.
Macron has embarked on a bid to bring Russia in from the cold, hosting President Vladimir Putin for talks in southern France last month and renewing high-level diplomatic contacts.
The two men spoke by phone on Sunday, hailing an exchange of 70 prisoners between Russia and Ukraine as a step forward in peace efforts.
They said work was continuing for a summit of the leaders of France, Germany, Russia and Ukraine in Paris later this month.
As the ministers began the four-way talks, Russia's top diplomat Sergei Lavrov welcomed France's efforts to rebuild relations, in particular remarks made by Macron that the time had come to "rethink our ties".
Le Drian said he and Parly were in Moscow to start a "frank discussion" in order to "move together towards a new architecture of confidence and security in Europe".
Macron's office said in a statement on Sunday that the ministers would be working on a roadmap for improving ties.
Ukraine will be the key issue, with Paris looking for signs that Putin -- and Ukraine's new president Volodymyr Zelensky -- are ready for more compromise after five years of conflict.
Iran is also likely to come up, as France and Russia look to save the unravelling nuclear deal with Tehran.