France was chosen for Putin's visit because it will take over the presidency of the European Union on July 1.
Medvedev will make his European debut in Berlin in early June when he will meet Angela Merkel, Germany's chancellor.
Following the talks with Fillon on Thursday, Putin sidestepped questions on whether Russia would be prepared to help France and other consumer nations cope with soaring oil prices.
In a news conference with the French prime minister, Putin said: "Russia is not the one setting the price of oil, but the market.
"If Russia were setting the price, then I think we could agree, but that is not the case. Not yet."
Earlier this week, France urged its partners in the Group of Seven industrial nations to press oil-producing nations to increase their output in a bid to bring down the price of oil, which has hit record highs of more than $130 a barrel.
Russia is the world's second largest producer of oil and the number one supplier of natural gas.
Russian officials said earlier on Thursday that Putin would be discussing plans for a new EU-Russia pact and Moscow's relations with Nato.
On Monday, EU member states approved the launch of negotiations with Russia on a new partnership and co-operation agreement, putting an end to two years of acrimony over the issue.
Medvedev is due to host the launch of negotiations on the pact in June at an EU-Russia summit in the Siberian city of Khanty-Mansiisk, just before the start of the French EU presidency.
At a Nato summit earlier this year, France opposed offering speedy membership of Nato to the former Soviet republics of Ukraine and Georgia, saying there must be discussion with Russia on such a move.
Georgia and Ukraine have applied for a Membership Action Plan, which prepares nations for entry into the military alliance.
The Russian officials said that Putin would also discuss the implications of a US defence missile plan, to be stationed in eastern Europe, which Moscow fiercely opposes.
On Friday, the prime minister is due to tour a Cossack museum outside the French capital and pay a visit to the Paris home of French writer Maurice Druon, 90, whose works are popular in Russia.
Putin and Druon, whose father was Russian, have met several times including at the writer's summer home in the Bordeaux region in 2003.