I agree with @TomD8 , a student is only exempt from FICA, if they are a W-2 employee of the college. The schools know this and will usually not withhold social security and Medicare tax.
On the other hand, I also agree with @Opus 17, if the internship is provided by the school, for credit, the 1099-NEC is not the correct way to report it. The student could report it as scholarship income, rather than self employment, and avoid SE tax.
The original poster doesn't say who provided the internship. If a third party, Schedule C is probably correct. A case could be made for the one time gig exception; SE tax could be avoided, but then the "other income" wouldn't be "earned income" for purposes of calculating the student-dependent's standard deduction. Of course, the 1099-NEC is going to be a "red flag" with the IRS.
