Connotations regarding F grade
As F stands for failing, of course there's a stigma associated with it. How much depends on the course in which it's received. For example, failing freshman biology matters much less if you're in art than if you're planning on applying for medical school. 

Also note that different schools handle repeated courses differently. Some schools count only the last grade, while some count both equally in the final average (a zero plus whatever an "A" grade counts as).