I have been dealing with this issue for a while now. It is a user/group issue. suPHP will fix this issue. I have not installed it yet.
You can also access your files using the Joomla component joomXplorer. It logs in as apache/apache, where your ftp accesses your file system as user/pascln.
As obeone said, the solution is mod_suPHP. In our guide (see signature) will help you to install and also Power Toys will help you to manage it from PLESK.
It was tested specially on Joomla, Info At Hand, but will work also for picture galleries, or any other solution where you have a lot of file uploads.