Sir Francis was the son of Edward Moore of East Ilsley in Berkshire, by his wife, Elizabeth Hall, an heiress from Tilehurst (Berkshire). He was educated at Reading Grammar School before entering St. John's College, Oxford, as a commoner in 1574. Francis continued there until nearing Batchelor's Standing, when he moved on to the Middle Temple and became a barrister. He was noted for his great proficiency in his profession and the integrity of his dealings.

Francis married Anne, the daughter of William Twitty Esq., of Boreham in Essex, at the end of Queen Elizabeth's reign, by whom he had three sons and four daughters. Needing a home to raise his family, he purchased the manor of South Fawley (Berkshire) from Nicholas Radishe Junior in 1594. Around the same time, he was, several times, elected a Burgess and also to a seat in Parliament, where he was a frequent speaker, first for Boroughbridge in Yorkshire (1589) and subsequently for Reading (Berkshire)  - between 1598 and 1614.

In the run up to the attempt, by the 'Gunpowder Plotters', to blow up Parliament in 1605, Francis had occasion to often work late with a client in London. It is recorded that, during this period, he saw one of the chief conspirators, Thomas Percy, leaving the home of the Earl of Salisbury, Head of the Secret Service, on a number of occasions in the small hours of the morning. He said nothing to anyone at the time, but it now seems that he was a key witness to the fact that the plot had been infiltrated by the Government and was encouraged for propaganda reasons.

Later, Francis became Counsellor, and Under Steward, for several years, at the University of Oxford, which conferred upon him the degree of Master of Arts in 1612. Two years later, he was made sergeant-at-law and, on 17th March 1616, received the honour of Knighthood at Theobalds (Hertfordshire) from the hand of King James. By 1618, he had added the manor of East Ilsley to his estates and obtained a licence to hold a sheep-market there. Over the next three hundred years, this market became famous as the largest in the country!