“They are advancing pawns here and everywhere; they want to show that there is only one Russia, the Russia of Putin,” said Alexis Obolensky, vice president of the Association Culturelle Orthodoxe Russe de Nice, a group of French believers, many of them descendants of White Russians who fled Russia after the Bolshevik Revolution of 1917. They want nothing to do with a Moscow-based church leadership headed by Kirill, patriarch of Moscow and All Russia, a close ally of the Russian president.

A Broader Push

The French Orthodox association is instead loyal to the ecumenical patriarch of Constantinople, a rival church leadership in Istanbul that has provided a haven for many of Mr. Putin’s churchgoing foes. After a long legal battle with Moscow, Mr. Obolensky’s association in 2013 lost control of Nice’s Orthodox cathedral, St. Nicholas, to the Moscow Patriarchate, which installed its own priests and rallied the faithful behind projects to warm France’s frosty relations with Russia.

When Russian church staff and their lay French supporters broke into the Nice Orthodox cemetery in February and declared it Russian property, allies of Mr. Obolensky hoisted a banner on the iron gate: “Hands off, Mr. Putin. We are not in Crimea or Ukraine. Let our dead rest in peace.”

Moscow’s quest to gain control of churches and graves dating from czarist times and squeeze out believers who look to the Constantinople patriarch is part of a broader push by the Kremlin to assert itself as both the legitimate heir to and master of “Holy Russia,” and as a champion of traditional values against the decadent heresies, notably liberal democracy, promoted by the United States and what they frequently call “Gayropa.”

“The church has become an instrument of the Russian state. It is used to extend and legitimize the interests of the Kremlin,” said Sergei Chapnin, who is the former editor of the official journal of the Moscow Patriarchate, the seat of the Russian Orthodox Church and affiliated churches outside Russia.

Unlike the Catholic Church, which has a single, undisputed leader, the pope in Rome, the Orthodox or Eastern branch of Christianity is divided into more than a dozen self-governing provinces, each with its own patriarch. The biggest of these, the Russian Orthodox Church, covers not only Russia, but also fragile new states like Moldova that formerly belonged to the Russian and later Soviet empires.

“We have been independent for 25 years but our church is still dependent on Moscow,” complained Iurie Leanca, a former prime minister of Moldova, who in 2014 signed a trade and political pact with the European Union that the church and the Kremlin worked hard to derail.