It was not immediately clear why France made an exception for the minister, who headed a Russian delegation to an assembly of the World Organisation for Animal Health in Paris that started on Sunday, Reuters wrote.
Germany refused him an entry visa in January.
Some politicians in France have voiced support in favour of lifting sanctions against Russia.
Read alsoMP calls on SBU, MFA to declare Gorbachev persona non grataLast month, France's lower house of parliament voted in favour of lifting European Union sanctions against Russia in a non-binding vote that went against the Socialist government's recommendation.
Tkachev's name was added to a list of Russian individuals banned from entering the European Union in mid-2014, when he was the head of Russia's southern Krasnodar region, because he was awarded a medal "for the liberation of Crimea" by the acting head of Crimea for the support he provided.