You need a library that provides an API to access the FTP server and return the necessary information regarding the files present on it. Then every time your application runs, it will connect to FTP, read the information about the files (timestamp, etc.) and inform the user if there is any novelty regarding the file stored locally.
Try for example the Apache Commons FTP client: http://commons.apache.org/proper/commons-net/
Observing: This may not be the best way to do this. The ideal, I believe, would be to provide a web service that brings the information of the files stored on the FTP server. Then who gets information from the files is the web service and not the Android application (either via FTP connection or by reading the data from the local files, if the application server that provides the web service is on the same machine as FTP). A connection to FTP to download the file would only be done if there was really need to download it.