F-1 visa holders are students. Their visas allow them to attend an accredited school in the U.S. There are very strict rules regarding (paid) employment by F-1 visa holders. The student would need an employment authorization card to work off of campus. You should discuss the situation with the International Student office at the students' school. Or, contact a qualified immigration lawyer in your area. You can find a qualified immigration lawyer at www.ailalawyer.com.
My response to your question is for informational purposes only, and is not legal advice, nor does it create an attorney-client relationship.
You are correct that you do not have to sponsor international students like H1b workers, just as you would for any other student, you would have to check F-1's authorization to work before you could employ them on internship.
Employment of international students remains strictly regulated during semester, in summer and also after course completion even after rules are relaxed regarding F1 student employment. Best Wishes!
My answers are for general information only, NOT A legal advice because these are not tailored to your specific situation. Contact an Immigration Attorney if you need legal advice.