In the UK, we almost always use the verb "to watch" for a movie (or a film), whereas I believe that in the USA people generally "see a movie".
However, if someone asks you "What are you doing this evening?", you can reply "I'm seeing a movie". In that context, you would be using the present continuous to indicate the future.
Having said that, if someone called you while you were at the cinema and asked "What are you doing?", you would also be able to answer "I'm watching a movie/film". You would be using the present continuous here. I agree that I don't think "I'm seeing a movie" would normally be used in the present continuous in that situation.
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