I don't really have any experience with Front Page, but from what I know it does feature some kind of insert function to integrate video into your website. This probably just creates the kinda old-timey HTML version of putting video clips into your site, which will then play via Windows Media Player. If you go with this solution, you might want to choose a suitable export format from Movie Edit Pro, like Windows Media Video (WMV) with a suitable bitrate for online streaming. The file would also have to be hosted on your server for the HTML page to access it. So, once you upload your project to the web server (e.g. via FTP), make sure to include this file, if Front Page doesn't take care of that automatically.

This solution might work for you, but it's not really anything very fancy or cutting-edge. Maybe you would consider an alternative of hosting your videos on YouTube and using the embedding code YouTube produces to integrate the video into your site as a little Flash video player. This might be a pretty neat solution and you also wouldn't have to worry about hosting the video on your own webspace. For your upload to YouTube, different export formats from Movie Edit Pro would do the trick. WMV might also be a good option here.