FTP was invented with US-ASCII as character set in mind, so it lacks a concept for different character sets at all. The server sends filenames as-is and the client has to properly interpret them.
FileZilla can do that as well: Add your site to the Site Manager (File then Site Manager…). For your site, go to Charset tab and select Use custom charset. As I do not know how the accepted character set name is, you have to try a bit: cp-1251, windows-1251, cp1251, etc.
If possible, make sure the FTP server supports UTF-8 and then always use UTF-8 (Unicode). This way you do not have such problems anymore.
ASCII and binary modes by the way are completely unrelated to character sets - see FileZilla Wiki regarding data type for more information.