I presume what you mean is that you normally hear 'What time is it?' and that you were surprised to hear 'What hour is it?'
And to answer your question - no, this is neither a natural nor a normal English way of asking this. No native speaker would ever use this form.
The character in the film may have been a non-native, such as a Spanish speaker, and the use of 'foreign-sounding' English was deliberate.
Or was it a historical drama? One possibility is that it was a story set many centuries ago, and the scriptwriter used a deliberately archaic-sounding expression to give an old-fashioned flavour to the dialogue.