The Video module for Drupal 6 has an option to use videos uploaded through FTP. The Drupal 7 version does not have that option. How can I embed large self hosted Video files?
To answer your question: Use the contributed Drupal 7 Video module.
You will likely need to configure your server to allow for large file/video uploads.
Most likely you will need to modify your PHP.INI file to allow large uploads. Specifically max post size and max upload size.
As for a widget that allows you to select a file uploaded via FTP, I see several issues in the Video modules issue queue that look relevant, but no solutions seem to be offered.
This question was also un-answered months ago. If FTP is a requirement you may need to write a custom module or contact the Video modules maintainers for a status update.
This is old question but nowadays there is solution for adding videos which are uploaded with FTP to server.
Solution is to use FileField Sources module. After this module is enabled then go to Manage fields in your Content type which has Video-field. Edit Video-field settings and you can find File Sources from there. Choose desired ways to add video for example File attach from server directory.