"Turquoise," or "Biryuza," features Depardieu as a man who travels to Russia after his son is killed there, RIA Novosti reported. Hurley plays Depardieu's former girlfriend, who becomes involved in his quest.
Depardieu, 64, recently received a Russian passport after giving up his French citizenship, saying he was doing so to avoid a new tax rate of 75 percent on the highest incomes.
A representative of the Chechen culture ministry said scenes featuring Hurley were being filmed in Grozny Saturday, with Depardieu expected to arrive next week. Actors from the Serlo Youth Theater in Chechnya are also featured in the movie.
Some scenes will be filmed in Moscow.
Depardieu visited Chechnya last year, attending Chechen leader Ramzan Kadyrov's 36th birthday party. He was also in Grozny in February when Kadyrov gave him a five-room apartment.
Notable deaths of 2014 [PHOTOS]