French was the diplomatic language of Russia, and the Russian nobility used it often, sometimes more fluently than Russian. In older books you'll even find the suggestion that Russian nobility couldn't speak Russian well, or at all . . . this is an exaggeration, but in general you'd find Foreign Ministry officials speaking French rather than Russian for official and even social purposes. This persisted despite wars with France-- the Russian Government signing the Alaska Purchase in 1867 had been at war with France in the 1850s.

With a Treaty, both versions of the text are "the Treaty" and misunderstandings or differences between the two texts are a problem (see the Treaty of Waitangi for an example where the English text is substantially different from the Maori text). At a practical level, few American diplomats or lawyers would have been equipped to judge the congruence of a Russian text with an English one.

Indeed, Russian diplomats struggled to find Russian language diplomatic boilerplate-- Europe had a vast archive of French (and Latin) legal formulas, but when you move to a language where you haven't written such a document before, you're stuck writing "new language", always perilous for lawyers. A famously difficult Treaty was that of Kuchuk-Kaynarca between Russia and the Ottoman Empire; texts were in Russian, Italian and Turkish, with Italian the controlling language. This choice is due to the prominence of Italian dragomans as translators in the Ottoman Empire; neither the Russians nor the Turks could have confidence that their reading of the other's text was precise, and indeed there are meaningful differences them. Ambiguities in thes readings contributed to the Crimean War . . .

See

The French Language in Russia: A Social, Political, Cultural, and Literary History

"Russian Skill and Turkish Imbecility": The Treaty of Kuchuk Kainardji Reconsidered