The Longest Day (1962)
The original trailer of the movie
Mike B. suggests that The Longest Day might be a better suggestion. It looks at the invasion from the American, British, French and German perspectives, among others. It is certainly more global in its scope than Saving Private Ryan or even Band of Brothers. One of my criteria for picking these movies was that they looked at patriotism as something more than just xenophobia wrapped in flags and bunting. The Longest Day certainly meets my standards on that criteria.
One comment by another teacher is that Saving Private Ryan is a more 'user-friendly' piece to historically analzye with his students. Its story is personal and not as epic as The Longest Day. This is an interesting discussion to me-what works best for our charges. Keep it up the discussion and I will post.
I will be honest that it has been quite a while since I've watched The Longest Day so I wanted to be fair to it. I will watch it in the next couple days and weigh in.