Strictly speaking, Franklin's wife was not "Lady Jane Franklin" ~~ Lady+Forename+Surname is the courtesy title of the daughter of a Duke, Marquess or Earl. (His heir, eldest son, would be known by his father's second title; a younger son of a Duke or Marquess would be Lord+Forename+Surname ~ think of famous detective of Dorothy L Sayers, Lord Peter Wimsey, whose elder brother was the Duke of Denver & sister was Lady Mary Wimsey - younger son of an Earl is The Honourable Forename+Surname.)

The wife of a knight, baronet, or junior peer would be simply "Lady Franklin"; if necessary to distinguish her from wife of others of same surname, she could be referred to, informally, as "Jane, Lady Franklin"; or, in writing, as "Lady (Jane} Franklin". But, properly speaking, her title would be simply "Lady Franklin".

~Michael~