Not merely correct, actually preferable! 'See' with 'movie' tends to occur mainly in the past tense, e.g.
I saw a good movie yesterday.
or the future
We're going to see a movie tomorrow.
but in other forms, including hortatives such as 'Shall we...?', 'watch' tends to be more common.
In some cases, most notably the present progressive with real present reference, 'see' verges on unacceptable, thus
A: What are you doing at the moment?
B: I'm watching a movie.
(rather than: ?...seeing...)
Student or Learner