No, Benjamin Franklin did not sign the Bill of Rights.
To understand why, we need to look at the timeline of events. The Bill of Rights, which consists of the first ten amendments to the United States Constitution, was proposed in 1789 and ratified in 1791. At that time, Franklin was already quite elderly and had passed away on April 17, 1790.
Franklin was, however, a prominent figure in the founding of the United States and played a significant role in the early political landscape. He was present during the Constitutional Convention in 1787 and signed the United States Constitution. Nonetheless, his absence from the discussions and ratification of the Bill of Rights is simply due to the fact that he had died before it was formulated and adopted.
In conclusion, while Benjamin Franklin was instrumental in many foundational aspects of the United States, he did not have the opportunity to sign the Bill of Rights as it came after his time.