Born in London, Jack Henry-Francis developed his early football at Fulham's academy before making the switch to Arsenal at the age of 12 in August 2016. He signed his first professional contract with the club in October 2021 and went on to represent Arsenal's under-21 side across several EFL Trophy campaigns, scoring his first goal in the competition during a 5–0 away win against Exeter City in October 2023.
A composed, box-to-box midfielder, Henry-Francis gained his first taste of senior professional football during a loan spell with Sligo Rovers in the League of Ireland Premier Division in the second half of 2024, making his competitive debut in the FAI Cup against Cobh Wanderers before featuring in league action. He was named on Arsenal's first-team bench for a Premier League fixture against Brentford in April 2025, marking a notable moment in his development, before departing the club at the end of his contract in June 2025.
Henry-Francis qualifies for the Republic of Ireland through his parents, who are from Mayo and Leitrim respectively, and has represented the country at under-19 and under-21 levels.
He joined Shelbourne on a multi-year contract in July 2025, where the League of Ireland club will look to him as a regular contributor in midfield. He marked his time there with an 88th-minute winner away to Cork City in October 2025, underlining his ability to make an impact in key moments.