It depends. Some parts of Franklin might be based on real events or people, but it could also have fictional elements added for entertainment purposes.
I don't think Franklin Murray is part of DC Comics. DC has a vast array of characters, but this name doesn't ring a bell among the popular or established ones.
The Benjamin Franklin kite story is based on historical events and is considered true. It's a well-documented part of his experiments and contributions to the understanding of electricity.