I don't see why users' native language would matter directly (I'm not a native English speaker, nor do I live in an English-speaking country, but I think I watch more movies in English than in my native language), but their location does, since not all movies get worldwide distribution even now.
You can get a rough idea of where people are coming from by looking at location fields in profile. For launched sites, you can analyse this kind of data on the Stack Exchange Data Explorer. This query (lightly adapted from one by David Freitas) shows a breakdown of users by country. Note that this is a very crude approximation, since it relies on data that users are free to enter or not and the query is far from recognizing every place name.
Looking at a few launched sites (beta sites aren't available in SEDE), Photography, Cooking and Gaming all have roughly half their users from mainly English-speaking countries (US + UK + Canada + Australia). That's a majority but not an overwhelming one; it doesn't warrant specifically tagging non-English-speaking movies as foreign.
So should we tag movies by country of origin? I do see some merit to the idea in principle, not exactly by country but by distribution channels, so that people can concentrate on tags that correspond to the distribution channels that they have access to. (Released in the US, released in India, etc.) However there are more and more international distribution channels: DVDs shipped by mail, video-on-demand, TV broadcasts… So this tagging would not be useful for very many people. And in any case I don't foresee that the community will keep it up.
On balance, origin tags would not be very useful and would be missing often anyway. So no, I don't think we should have origin tags.
We might have origin tags in a different form: hollywood, nollywood, cinecitta…; these could make sense in that they imply a certain category of style of movie, but they are terribly broad.