"We have differences, but we also have mechanisms to establish a dialogue," the French politician said, speaking with Russian senators at the Federation Council of Russia.
Leconte added that the two countries could get back to the discussion of a visa-free regime.
France and Russia should also work together in the fight against ISIL in Syria, Leconte said, adding that France is receiving up to 10,000 Syrian refugees every day.
The Mistral sale was supposed to be the biggest arms sale ever by a NATO country to Russia, until the deal fell apart because of the Ukraine crisis.
To conclude his talk, Leconte asked Russian senators to help an Alliance Francaise representative in Russia's Irkutsk who's currently under an administrative investigation and whose visa is expiring at the end of October.
Leconte's visit to Moscow isn't the first time French politicians have come to Russia. Earlier this year the group of ten French lawmakers visited Crimea to get a sense of what was really going on in the Black Sea peninsula following its secession from Ukraine in March 2014.
