Serving as secretary to the Paris embassy, Vernon became a key link between French and English scholars, copying important works for the Royal Society.
In 1668, he was chosen because of his experience to accompany Charles Howard, 1st Earl of Carlisle, ambassador-extraordinary to Sweden, and the king wrote to Christ Church requesting a leave of absence for him.
In 1670, Christiaan Huygens, seriously ill, chose Vernon to carry out a donation of his papers to the Royal Society in London, should he die.
Vernon copied the Mésure de la terre of Jean Picard for the Royal Society, which therefore saw it in 1671, while Colbert communicated it officially in 1676.
[4] Among Vernon's other correspondents was Edward Pococke, copies of whose son's Latin version of Ibn-al-Tifail he presented to the Sorbonne and to Christiaan Huyghens.
Another correspondent was John Collins, for whom Vernon obtained books through Jean Berthet, including works by René Descartes and Blaise Pascal.
Vernon's services were recognised by his election to the Royal Society on his return to England in 1672, his proposer being Henry Oldenburg.
Spon had seen a recent account by the Jesuit Jacques Babin and wanted to compare Guillet's book with the facts on the ground.
A letter to Oldenburg, dated 10 January 1675, was printed in the Philosophical Transactions of 1676 as Observations made during Travels from Venice through Dalmatia … to Smyrna.
It was translated into French by Jacob Spon, who incorporated it in his Réponses à la Critique publiée par M. Guillet, 1679.
Combined with notes of Jacques Carrey, the observations of Vernon were used by William Bell Dinsmoor in his Parthenon reconstruction, in relation to the south frieze.
[16] A Latin poem entitled Oxonium Poema, published in 1667, under the initials "F. V. ex æde Christi", has been identified as by Vernon.