I can help a little bit with this.
The three men represent the origin of the nation of Switzerland. In 1291, what are now the Swiss Cantons of Uri, Schwyz, and Unterwalden united in a pledge of mutual defence, commerce and friendship. Switzerland is officially "the Swiss Confederation" with the Swiss German word for confederation being "Eidgenossenschaft" or more literally, "oath fellowship". That is what is depicted in the three men symbolizing the original three cantons, the taking of the oath.
The tower on the left is actually a Roman Fasces like what is on the reverse of the
Mercury dime. Since Roman times the Fasces has been a symbol of strength through unity.
"La Societe des Suisses" is French for The Society of Switzerland. I can not help with the hands or the "6" but the hat, crossbow and arrow through the apple are all as you say, definitely William Tell attributes.
My guess is that it is not a Shooting medal but rather a token or a commemorative item for some other purpose. It is very patriotic. Perhaps La Societe des Suisses was a Swiss patriotic organization of some sort or even an organization of Swiss expatriates in some other country.
A very interesting item!