What programming language to learn when developing a video software program?

Learning a language and building a video editor are two different learning curves. Also the development of the user interface for the editor and what happens in the background are two separate tasks.

To develop it, it is necessary to understand different stages / processes of what really happens in the background when we perform some action in a video editing software. http://www.videolan.org/vlmc/ may have some resources related to it. This is the most important.

Then comes the choice of the programming language that depends on the processes and the learning curve associated with it. It may be that you need more than one technology. For example, you can use any existing library, if available, to achieve part of it instead of writing it.

I guess Java would be the preferred language if you want to start programming and there are some libraries available related to http://stackoverflow.com/questions/809646/libraries-tutorials-for-manipulating-video-in-java

You can check the code of any open source video editor: http://www.smallbusinesscomputing.com/ProductReviews/Software/5-best-open-source-video-editors-for-small-business.html

http://www.videolan.org/vlmc/ seems to use the language C.