"I watch movies sometimes."
So it looks like both ときどきえいがを見ます & 映画を時々見ます are accepted. Is the meaning changed here? To me it sounds like "Sometimes movies I watch" vs "Movies I sometimes watch" with the latter making more sense to me. What would sound more natural and is the meaning / emphasis changed?
が marks the subject; the one doing the action
時々映画が見ます would say "Sometimes movies watch (something)", with "movies" being the thing watching, rather than the thing being watched.
The direct object (the thing being acted on; 'watched') is marked with を, which is the preferred translation here.