Chanson (the word is pronounced "шансон"/"shanson" in Russian) is popular in Russia. But keep in mind that the genre which is often called "Russian chanson" is very much different from its French counterpart. It evolved from criminal songs, which is also an old and popular (among certain people) genre in Russia.
Here's a nice article about Russian chanson and its main themes: Russian chanson - Wikipedia, the free encyclopedia
French chanson: Chanson - Wikipedia, the free encyclopedia