Relax. One F will not ruin your chances of getting into law school. Your GPA will barely be affected. A single point on the LSAT will probably have a bigger effect than a single F.
I never received a B, let alone a C, in any of my classes, but I'm terrified that this F will ruin my life.
Then be prepared for the shock of law school grades. No, seriously. Read up on it, talk to people in law school, etc. Getting A's in law school is the exception, not the norm. Grades are on curve and most people are a little shell shocked after the first semester.
I'm not saying this to be a jerk, but you sound a little overly concerned with grades and you seem to have greatly overestimated their impact on your life. It's alright, many college students do this. But, if you're this freaked out by grades then you need to understand what you're getting in to in terms of law school.
You're going to read a lot of stuff on the internet telling you that unless you graduate in the top 10% of your law school class you'll be flipping burgers, etc. It's BS, but you'll read it anyway and it seriously stresses out a lot of people. To paraphrase the great Citylaw, there is a 90% chance you won't be in the top 10%.
Undergrad is pretty easy. I know it may not seem like that now, but wait until law school. You'll see what I mean. I think it is therefore good for your emotional well being to understand how law school works before investing in it.