Tchaikovsky wrote a passage from the Russian national anthem into the 1812 Overture, as well as the French.
Both national anthem pasages are somewhat anachronistic however, as Tchaikovsky used the tunes that were current in his own time, not in 1812.
Russia didn't even have a national anthem until 1816, when Prayer of the Russians was chosen – sung to the tune of God Save the King. Then in 1833, Tsar Nicholas I chose God Save the Tsar! to be the anthem of Imperial Russia; this is the one that Tchaikovsky used. It was replaced in 1917 by the Internationale, which was used until 1944 when the Communist International was dissolved in order to enable the Soviet Union to maintain its alliance with its allies of World War II, and this necessitated a new anthem.
The Marseillaise was chosen as the French national anthem in 1795, but it was banned by Napoleon in 1805 and would not have been played during his Russian campaign. It was reinstated as the French Anthem in 1879 – the year before the commission of the 1812 Overture. The unofficial anthem that was used in Napoleon's time was entitled Veillons au Salut de l'Empire.
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