If you are looking for some experience in this matter. You already had it and now just need to make sure you learn from this event. First you should realize that the furnace blower uses a lot of juice, typically about 7 amps. That pull can run down a battery bank quickly. Many appliances such as a refrigerator or furnace will shut down when the battery voltage drops less than about 12 amps.
Another learning lession you may encounter is battery life. Even a deep cycle battery will not last long if you run it down all the way. I typically replace my car or RV batteries anytime I have an incident and run them flat.
Odds are your furnace will start to work again after you charge the battery more. If not I would pull the fuse and then reinsert. That will likely reset. Personally I would not even try that until the battery charge was about 12.5v or so. Again, I would also consider replacing the battery. If you plan on running the furnace a lot, you will need shore power or frequent charging from a generator or solar system.