So I started using Git together with this workflow to make a personal website (mostly for testing and to learn Git) and I am developing it locally on my laptop using Xampp.
If you have no SSH access to the remote server and the hosting provider doesn't offer a git deploy feature, you won't be able to deploy directly using git.
However, it's always a good idea to track your source code regardless the remote options.
In your case, a good alternative to automate the release process would be to create a simple deploy script in your favorite programming language (Ruby, Python, Bash...) that loads the list of changed files from your git repository and performs an upload via FTP of these files.
A simple search for git-ftp reveals that there are already two projects that seems to do what I suggested: