I would like to know if there is an easy way to push a GIT repository into production (on a FTP server) ?
Some tools recently added to the Git wiki:
git-ftp by René Moser is a simple shell script for doing FTP the Git way. Use git-ftp.sh to upload only the Git tracked files to a FTP server, which have changed since the last upload. This saves time and bandwith. Even if you play with different branches, git-ftp.sh knows which files are different. No ordinary FTP client can do that.
git-ftp by Edward Z. Yang is a simple script written in python for uploading files in a Git repository via FTP, only transferring new files and removing old files.