Yes, Ben Franklin succeeded in drafting the Declaration of Independence based on reason and the only time we see people questioning our founding documents is when people don't understand them. We should first understand that these old documents were written at a different time with a different set of beliefs. At the time, he wrote a wonderful declaration.
In 1754, at a meeting of colonial representatives in Albany, New York, Franklin proposed a plan for uniting the colonies under a national congress. Although his Albany Plan was rejected, it helped lay the groundwork for the Articles of Confederation, which became the first constitution of the United States when ratified in 1781.
Ben Franklin modeled the Declaration of Independence on the French ideas of natural rights. That is, that people have inherent worth because they are people. This was a unique document at the time. Although passionate about his stance, Franklin was very logical and objective. This logical approach is apparent in a number of Franklin's writings and his notable quotations.
Benjamin Franklin did not write the declaration of idependance. Thomas Jefferson did. He might have helped, but unless there has been some new information that came out recently proving that he actually wrote the Declaration of Independence he did not succeed at writing anything. But yes, the Declaration of Independence was mostly based on reason.