I applied to the combined honors English and Communications program, but didn't get in because my CMST 1A03 mark wasn't high enough (I missed the deadline for one of the major assignments ) . I still want to get into the program, but to transfer into it in second year will I have to take CMST 1A03 again and then re-apply? Or can I take the required level II CMST courses and then transfer and continue to fulfill the requirements for the program?

To be accepted into the combined program you must:

Completion of any Level I program and a Cumulative Average of at least 5.0 and a grade of at least C in CMST 1A03.

Do you have at least a grade of C in CMST 1A03? If yes then just do increase your GPA and apply again.
If you don't have a C then you must do the course again to apply to the program!