Although Franklin's style was part of the Age of Reason, I would argue that his subject matter began to cross over into Romanticism. Stylistically, Franklin is scientific. He holds to the rhetoric of the patriot and politician in most of his writings, avoiding the superfluous detail and emotion that would become such a part of the Romantics' work.
However, Franklin spoke about improving human existence and expressing individuality. His thirteen virtues was an attempt to achieve the most perfect human form and behavior. This desire to improve oneself and to examine the human condition is very much a part of Romantic literature, and would be revisited again in the works of Thoereau and Emerson.
Benjamin Franklin's writing style was clear and had appeal to many people, but it is not Romantic. Franklin is smack dab in the middle of the Age of Reason, or Enlightenment, when scientific observation and critical reason were paramount (see the eNotes article "Enlightenment," linked below). Whereas the Romantics believed that the individual could attain oneness with God through nature, writers during the Age of Reason either believed there was no god or saw God as a disinterested creator. Franklin was one of the latter. Like many other founders of the United States, Franklin was a deist. They believed that God created the world and everything in it and then sat back to watch what happened; that God does not become involved in people's lives. For further discussion, see the eNotes article "Romanticism and Religion," linked below.