Franklin's love of chess is well known (see here and here). Franklin admired the French, and, along with many other famous chess players, frequented the famous Café de la Régence chess club in Paris. His set, unsurprisingly, was in the French Régence style. In Franklin's time, the styling of the Régence differed slightly from the styling seen today> Changes to that styling came about no earlier than the C19th (this is corroborated through looking at the set in Diderot's late 18th century Encyclopédie--click for image--which still has the old forms). Régence sets were made in wood, bone and ivory--Franklin's was wood. The wood sets were almost always of boxwood for both the white and the black sides: the black was "ebonized". Boxwood is native to France, and was used widely.

The early Régence sets had these characteristics: