Hennigan graduated from Babson Institute Suffolk University Law School.

He was also the Democratic nominee for Massachusetts Attorney General in 1964, but lost to Edward Brooke.

His father James W. Hennigan Sr. also served in the Massachusetts General Court.

He was a driving force behind his daughter Maura Hennigan's unsuccessful 2005 attempt to become mayor of Boston.

However, Hennigan had been the leading advocate of trying to implement integration on the School Committee.