While I know it would most leap out to have some songs about Franklin for the musical 1776, instead I'm going with another Broadway musical, Ben Franklin in Paris. The show starred none other than Robert Preston and, though not successful still had a solid run of 215 performances, about half a year. It tells the story of Franklin going to France to try and raise money for the American Revolution. The musical opened in 1964 and has a score by Sidney Michaels and March Sandrich Jr. The songs are just fair overall, though there are several which are quite nice -- two of which I'll post here. (When the show was out of town, Jerry Herman was brought in to work on it, and added two songs, neither of which are these below.)
The first is my favorite, and happily there's video of it. "Half the Battle."
The second number actually had a little bit of a life outside the show, with several recordings, including one by Robert Goulet. "Look for Small Pleasures," sung by Preston and the female lead Ulla Sallert.