He was the son of Andrew Hay, 8th Earl of Erroll by his first wife, Lady Jean Hay, daughter of William Hay, 6th Earl of Erroll. He was the second eldest son, but his older brother Alexander, who was a deaf-mute, was declared "insane" and skipped in the succession. Francis succeeded to the earldom upon the death of his father in 1585.
Early in his life he converted to Roman Catholicism, and as the associate of George Gordon, 1st Marquess of Huntly joined in the Spanish conspiracies against the throne of Queen Elizabeth. In 1589, he began engaging in treasonous correspondence with King Philip II of Spain, who was also briefly King of England by his marriage to Queen Mary.
A letter he wrote to King Philip declaring his allegiance to Spain was intercepted and sent by Elizabeth to James VI. In February 1589, he was ordered to appear in front of the Privy Council. Failing to appear, he was denounced as a rebel.
He engaged with Huntly and Crawford in a rebellion in the north of Scotland, but their forces surrendered at Aberdeen on the arrival of the king in April; and in July, Erroll gave himself up to James, who leniently refrained from exacting any penalty. In September of the same year he entered into a personal bond with Huntly for mutual assistance; and in 1590 displeased the king by marrying, in spite of his prohibition, Lady Elizabeth Douglas, daughter of the William Douglas, 6th Earl of Morton.
Erroll was imprisoned on suspicion of complicity in the attempt made by James Hepburn, 4th Earl of Bothwell and Patrick Gray, 6th Lord Gray to surprise the king at Falkland in June 1592; and though he obtained his release, he was again proclaimed a rebel on account of the discovery of his signature to two of the Spanish Blanks, unwritten sheets subscribed with the names of the chief conspirators in a plot for a Spanish invasion of Scotland, to be filled up later with the terms of the projected treaty. After a failure to apprehend him in March 1593, Erroll and his companions were sentenced to abjure Roman Catholicism or leave the kingdom; and on their non-compliance were in 1594 declared traitors.
On 3 October they defeated at Glenlivet a force sent against them under the Earl of Argyll; though Erroll himself was severely wounded, and Slains Castle, his seat, razed to the ground. The rebel lords left Scotland in 1595, and Erroll, on report of his further conspiracies abroad, was arrested by the states of Zeeland, but was afterwards allowed to escape. He returned to Scotland secretly in 1596, and on 20 June 1597 abjured Roman Catholicism and made his peace with the Church of Scotland. He enjoyed the favour of the king, and in 1602 was appointed a commissioner to negotiate the union with England.
His relations with the Kirk, however, were not so amicable. The reality of his conversion was disputed, and on 21 May 1608 he was confined to the city of Perth for the better resolution of his doubts, being subsequently declared an obstinate "papist", excommunicated, deprived of his estate, and imprisoned at Dumbarton; and after some further vacillation was finally released in May 1611.
The dispute which began in his lifetime concerning the hereditary office of Lord High Constable between the families of Erroll and of the Earls Marischal was settled finally in favour of the former; thus establishing the precedence enjoyed by the earls of Erroll next after the royal family over all other subjects in Scotland.
- Mary, daughter of John Stewart, 4th Earl of Atholl
- Margaret, daughter of James Stewart, Earl of Moray
- Elizabeth, daughter of William Douglas, 6th Earl of Morton
By his third wife he had five sons and eight daughters:
- William, 10th earl
- Anne, married George Seton, 3rd Earl of Winton
- Jean, married John Erskine, Earl of Mar
- Mary, married Walter Scott, 1st Earl of Buccleuch
- Elizabeth, married Hugh Sempill, 5th Lord Sempill; secondly; James Douglas, 1st Lord Mordington
- Sophia, married John, Viscount Melgum, son of George Gordon, 1st Marquess of Huntly
- Margaret, married Sir John Seton of Barns
- Isabel, died unmarried
- Helen (died 1625, aged 10)
The earl died on 16 July 1631, and was buried in the church of Slains. The poet Arthur Johnston composed a poem in Latin for his funeral.