I think you would face the same outcome of redoing the class. Try contacting the admission officers of the other college and ask if they recognize the composition class from the college you currently attend. If they do not, then the F has no bearing and you will have to retake it if you choose so. Alternatively, if they recognize the course in general, it would be in your best interests to re-do it, either during the summer or normal school time because they probably would not recognize the fact you have completed it.

I assume you are in your first year at college, so if you plan to pursue graduate studies or research courses, the F would not hinder you if you improve it simply because it's a first-year course. The exception of course is if you wish to pursue a research course during your second year that is in the field of English or composition.

You are always able to indicate whether a grave event occurred during the course that caused the low mark. You would want to consider this especially if your other courses have roughly the same mark.