Medvedev, the former president who is considered less hardline than the current president Vladimir Putin, will head a delegation of ministers to meet French president François Hollande on Tuesday.
Diplomats say Syria is expected to dominate the talks.
“It is an issue where, there can be no doubt, we have some disagreements with France, but also some common views. Russia, like France, wants to find a political solution. The disagreements are over how,” Alexander Orlov, Russia’s envoy to Paris, told news agency AFP.
As the death toll grows to more than 40,000 following 20 months of conflict, countries such as France, the United States and Great Britain have been at loggerheads with Russia and China, who have blocked efforts at the United Nations Security Council to ratchet up the pressure on Syrian president Bashar al-Assad.
“The West says it [a solution] must start with the departure of Bashar al-Assad, and we say this is where it must end.”
Russia has accused Western powers of escalating the conflict by backing armed rebels and said plans pushed by Paris to provide the rebels with "defensive weapons" would violate international law.
Moscow has also criticised Turkey's requested deployment by NATO of Patriot missiles on its border with Syria, warning that the move raises the risk of expanding the conflict.
Aside from Syria, the talks are also expected to focus on economic and cultural cooperation, including, Orlov said, the possible purchase by Russia of French navy boats after its agreement to buy two Mistral-class warships from Paris.
Plans to build a Russian Orthodox church and cultural centre near the Eiffel Tower are also expected to be on the table.