Usually a good idea to be a member of the NRA - not strictly required, but they are the ones who maintain shooter classifications and national records, etc.
Find your state shooting association - they are usually the state-level affiliate of the NRA, and usually maintain a state schedule of matches, especially state/regional championships. The NRA also usually publishes a list of matches in Shooting Sports USA magazine, but since match directors can opt in or out as to whether to be listed... not all events may be in there. Through your state association you should be able to get a phone or email contact for the state High Power Rifle director - they should be able to point you in the direction of which ranges have regular Prone & F-Class matches.
Thats another point to be aware of... even if you find a schedule of matches, odds are good that not many will explicitly say 'F-Class', but you'll probably see a bunch that say 'Prone' or 'Fullbore' or 'Palma'. Generally speaking, since F-Class shoots alongside Prone/Palma, same distances, etc. just different targets, you can most likely shoot at any of the aforementioned events. Talking to that HP director will hopefully point you to ranges that have active F-Class participation, which will likely lead to a happier experience.