OK, by finding the Sportsman in an old reference I discover that it is the Model 11C. When I find that model in a newer book, it is indeed built under license from FN using the Browning Auto 5 patent. Suggested value in NRA Very Good condition is $250 and $300 in Excellent.
Remington traced its heritage to Eliphalet Remington, an early American gunsmith who produced his first flintlock rifle in 1816. Raised in Central New York, Remington purchased land along the Erie Canal in 1828 and established an armory.
Early 1909.
Early 1920.
Remington does not do factory letters.The Remington Society of America maybe able to help you at least date your firearm but most early records were lost in a fire and only some of the early percussion information was able to be pulled from military records and other very early firearms only can be dated by model and variation. (estimate)
Early 1912
1913 (early)
Early 1913
Remington Arms Co., Inc. Remington, once owned by a Delaware holding company, DuPont Chemical and Energy Operations, Inc., was sold to Raci Holding in the early 2000s.
Early 1911
Early 1911
Early 1914
You may be thinking of the Opening of the The Worldwide Sportsman which aired on ABC in the early 70's. There is a clip of it on YouTube. Search for ABC Worldwide Sportsman opening montage, and see if that is it. Good luck J