I can speak to your question indirectly–my daughter is a junior in Creative Producing at Dodge and my son will enter Film Production in the fall.
Internships are the backbone of becoming employable in the film industry so you are smart to be thinking along those lines so early! Not everyone does! Chapman has a career/internship center, but as a Dodge student you are far better off hustling and finding your own internships via the college’s Handshake account and networking with upper classmen by working on their sets or getting to know them in other organizations–mostly greek life, which isn’t as much of a party scene at Chapman as it is many places) and getting referrals to their internships. Get out and get involved in sets from day one–you can be on set every single weekend starting freshman year as a PA or Grip–NO MATTER WHAT YOUR MAJOR IS!!!
And again, it doesn’t matter what your major is for the internships! It matters that you HUSTLE and that you aren’t afraid of work. My creative producing daughter has had internships alongside film production majors, screenwriting majors and TWP majors. Also realize that most internships won’t start you out doing what you want to be doing (again, why the major doesn’t really matter). You need to get out there and learn how the industry works. Most entry internships will have you making a lot of coffee and answering a lot of phones. But you will also learn to do script coverage which is a key skill that most higher level internships will ask that you have experience in. What I am saying in a nutshell is you won’t get a writing internship right off the bat. Learn the ropes, work hard and that first internship will lead to more–they will refer you to ones that you would never find otherwise.
Screenwriting will give you all the skills to write for film or television. You can even write for TV during interterms in the “Byte Sized” pilot class. Plus all the TV courses are available to most majors so you can learn the business of it too. You can even pick up a minor in Television if you desire.