Charlie was born in Watford, making his way through Non-League football to success in the EFL with Scunthorpe, Northampton and Brentford.

He gained his first experience of senior football with Hadley, A.F.C. Hayes and Hendon between 2013 and 2015. He was a part of the 2014–15 Hendon squad which reached the Isthmian League Premier Division play-off final and won the 2014–15 London Senior Cup.

On 10 June 2015, Goode joined League One club Scunthorpe United on a free transfer and signed a two-year contract, with the option of a further year. He failed to fully establish himself during four seasons at Glanford Park and by the time of his departure in July 2019, he had made 85 appearances and scored six goals.

As a result of falling down the pecking order at Scunthorpe, on 31 January 2019, Goode joined League Two club Northampton Town on loan until the end of the 2018–19 season. During what remained of the season, he made 17 appearances and signed a three-year contract with the club for an undisclosed fee. Goode was named team captain for the 2019–20 season and made 45 appearances, scoring four goals during a campaign which culminated in promotion to League One. He was voted the club's 2019–20 Supporters' Player of the Year, was named in the League Two PFA Team of the Year and was nominated for the September and October 2019 PFA Fans' Player of the Month awards.

On 18 August 2020, Goode signed for Brentford for an undisclosed fee and signed a four-year contract, with the option of a further year. After a period out with illness, he returned to match play in mid-December 2020, but then spent another period out of the team in January 2021, until returning to full fitness in March. Goode made four late-season appearances, but did not appear during Brentford's 2021 EFL playoff campaign. As an unused substitute during the 2–0 victory in the Final over Swansea City, he received a promotion medal.

His 21/22 season was plagued by injury and limited him to just 14 games in a Brentford shirt. His Premier League debut came against Norwich City on 6 November 2021.

For the second half of the season, he was sent on loan to Sheffield United as The Blades pushed for the Championship Play-Offs. After two games, a leg muscle injury forced his return to The Bees.