what would be some best practices for boosting ones chances of getting an internship at a major company in the film or music industries?
This may be a bit broad, but the logical way is to foster your skills on music, filming, etc., so your profile may stand out more in the eyes of possible recruiters of such industry.
Besides that and perhaps a recommendation from someone relevant in the industry there are few things you can do; as in any job the applicants should be measured on their skills and knowledge, so the best you can do is to prepare yourself for working in such industry (take courses on Music, or Film editing, etc.).
What is the most appropriate way to reach out to companies?
Check for companies that you would like and see if they have any job opening or are hiring people. You can then proceed to apply to the ones you like.
You can also go the other way round, and look for job openings on that industry regardless of what company it is, and then do some research on them to decide if it's worth applying.
Also, you could try with a contracting firm or similar, some that can contact you with jobs or companies in the music or film industry and help you in the job-seeking process.