Most any engine exhaust can trigger an LP detector, so can aerosol sprays, doggie farts, many cleaning products, etc. It's not a very discriminating device. However, wood smoke would not usually set it off. Could be some other stuff in the fireplace, though, e.g. food, plastic wrappers, beverage cans, etc. Those can add enough hydrocarbons to set it off.
Once when a neighbor was working on repairing/tuning an old lawnmower, he kept setting off my LP detector. He fiddled with the thing for a month or so and I finally turned the LP detector off in self-defense.