1. If you let your friend drive your car, if there is car accident, and if it is your friend's fault, it goes to your insurance policy, and your insurance will....
2. If you rent a car (from any car rental company), you have to agree (and sign) you are responsible for all traffic tickets. If you fail to do so, car rental will charge to your credit card, plus administrative cost.
3. Your friend must be a very good friend of yours (since you let him/her drive your car).
Since your friend paid the fine, you can decide in future whether you let your friend drive your car. There is no right or wrong, it is between friends (really good friends).