Francis Cooke and Hester Mahieu had five children. John, Jane, Jacob, Hester and Mary. Their son, Jacob also had a son named Jacob who married Lydia Miller and this couples' first child was named William b. Oct. 4, 1683
William Cooke married Tabitha Hall. They had seven children including a son, William born 15 Jan. 1714/5: died Kingston on 18 April 1731 in his 17th year.
You may want to check the five generation book on Francis Cooks' descendants. I have not seen the name Free associated with Francis Cooke before. When Francis Cooke and Hester Maiheu were married, there were Walloon witnesses, which may indicate a French Protestant connection.