Sent to England at a very early age, he was educated, first at a school kept by a Transylvanian in Great Queen Street, London, and afterwards by one Mr. Dalgarno at Oxford.
The States of Jersey, of which Falle, as Rector of Saint Saviour, was a member, made an appeal to William III for protection.
With another donation by Canon Dumaresq (died 1805), this benefaction developed into a large library, for which the States provided a building in Saint Helier.
Around the same time Falle edited a history of the campaign of the battle of Landen in the Nine Years' War, by his friend and colleague the Edward D'Auvergne, rector of St. Brelade.
In 1722 he contributed an account of the Channel Islands to Edmund Gibson's translation of Camden's ‘Britannia,’ and in 1734 brought out an expanded edition of his History of Jersey.