Born in Lewisham, London, to Ivorian parents, Nouble started with Chelsea in youth team football at under-12 level and was a regular in their youth team for the 2007–08 season. He made his Chelsea reserve team debut in November 2007.

In July 2009 he rejected the offer of a professional contract with Chelsea and on 21 July signed a five-year contract with West Ham United for an undisclosed fee. He made his Premier League and West Ham debut in their 2–0 away win against Wolverhampton Wanderers on 15 August 2009, coming on as a substitute for Carlton Cole. His first league start for West Ham came on 17 January 2010 in a 0–0 draw, away against Aston Villa.

Having previously been capped at England under-17 level Nouble made his first appearance for the England under-19 side on 8 October 2009 in a 3–1 victory against Finland under-19 in a UEFA under 19 championship qualifying round game in Slovenia.

He joined West Bromwich Albion on an initial one-month loan deal on 8 February 2010. He made his debut on 9 February 2010 at home against Scunthorpe United and made three appearances in total for West Bromwich Albion. He then joined Swindon Town in March 2010 on a one-month emergency loan deal as a boost to Town’s striking options due to injuries to Billy Paynter and Vincent Pericard. He made his debut for Swindon on 20 March against Norwich City. In April 2010 his loan was extended until the end of the 2009–10 season. He had made eight appearances for Swindon.

In September 2010 Nouble joined Swansea City on a three-month loan contract. Manager Brendan Rodgers said of him “…Frank has stature, presence, burning pace and wants to score goals. He has some Premier League experience and this is a chance for him to be part of a terrific squad and prove he can come and play and work well at this level.” He made his debut on 18 September in a 2–0 home win against Scunthorpe United, and scored his first goal in senior football on 28 September 2010 in a 3–2 win against Watford, coming off the bench to score with his first touch of the game. Following growing injury concerns at West Ham, Nouble’s loan was cut short in October 2010 and he returned to Upton Park. In January 2011, Nouble signed for Barnsley on loan until the end of the 2010–11 season. He made his debut the following day in a 2–0 win against Preston North End. In March 2011, Barnsley manager Mark Robins decided not to extend Nouble’s loan with Barnsley and he returned to West Ham. On 11 March 2011, Nouble joined League One club Charlton Athletic on a month-long loan. He made his debut for Charlton in the 0–1 home defeat against Brentford on 12 March 2011 and scored his first Charlton goal on 19 March in their 2–1 away defeat against Dagenham and Redbridge.

On 18 July 2010, Nouble scored twice for the Young Lions in their 3–2 defeat of Austria in the UEFA European Under-19 Championship being played in France. He made eight appearances in total for the under-19s.

On 15 September 2011, Nouble signed on loan for Gillingham for an initial one-month period, scoring on his debut as the Gills won 6–1 at Hereford United. Gillingham manager Andy Hessenthaler praised Nouble saying, “He looks good. He’s hungry and young and has decent pedigree with his Premier League experience and gives us another option.” After a successful first month his loan deal was extended by a further month. His loan was then extended by one final month until 17 December.

On 31 December 2011, Nouble scored his first and only goal for West Ham at Pride Park in a 2–1 defeat to Derby County. Two days before the January 2012 transfer window closed, League Two club Crawley Town made a bid for Nouble, which was accepted by West Ham United but rejected by the player. In March 2012 Nouble joined Barnsley for a second loan period, on a one-month loan deal. At the end of the 2011–12 season, Nouble was released by West Ham when his contract expired.

On 22 June 2012, Nouble signed for Championship club Wolverhampton Wanderers as a free agent, signing a two-year deal. He scored his first and only goal for Wolves against Northampton Town in the League Cup on 30 August. Nouble was rarely utilised, making just five appearances before his stay at Molineux came to an end.

On 8 January 2013, Nouble signed for another Championship club when he joined Ipswich Town for an undisclosed fee, believed to be around £25,000, signing an eighteen-month contract. He made his debut on 12 January, in a 0–0 draw against Cardiff City, and scored his first goals when he scored twice in a 3–0 win over Crystal Palace on 16 April 2013.

On 1 September 2014, Nouble signed for League One club Coventry City on a short-term loan from Ipswich until January 2015. He made his debut and scored his first goal for Coventry against Gillingham on 5 September 2014, a game which Coventry won 1–0.

On 7 January 2015 Nouble was released from his contract by Ipswich Town and signed a 6-month permanent contract with Coventry City two days later. He was released by Coventry at the end of the 2014–15 season.

On 15 June 2015, Nouble confirmed he had signed for China League One side Tianjin Songjiang on a two-year contract. He scored three goals during his time with the club as one of three foreign players in the squad. On 31 December 2015, Nouble was loaned to fellow China League One side Nei Mongol Zhongyou until 31 December 2016 but failed to make an appearance for the club after falling out of favour.

In October 2016, Nouble re-joined his former loan club Gillingham on a short-term contract. He scored his first goals of his second spell with the club in a 2–2 draw with Brackley Town of the National League North in the FA Cup on 5 November 2016. After three goals in 13 games, he was released by the club at the end of his short-term contract in January 2017.

On 18 January 2017, Nouble signed a short-term deal with Southend United until the end of the 2016–17 season following a successful trial. He made his club debut on 28 January as a substitute during Southend’s 1–1 draw at Fleetwood Town. He was released by the club at the end of his contract.

On 28 June 2017, Nouble signed a one-year contract with League Two club Newport County. He made his debut for Newport on the opening day of the 2017–18 season, scoring the first goal in a 3–3 draw with Stevenage. On 26 August 2017, he scored a 13-minute hat-trick in a League Two match versus Chesterfield, scoring the first three goals in a 4–1 win. He completed his season at Newport with his best return in a single season so far, ten goals in 52 appearances.

Following the expiry of his contract with Newport County, Nouble signed for League Two rivals Colchester United on a two-year deal on 8 June 2018. He made his competitive debut for Colchester on 4 August in a 0–0 draw with Notts County. He scored his first Colchester goal on 15 September in their 3–0 win against Cambridge United. On 28 April 2020 Colchester confirmed that Nouble would be released at the end his contract in June 2020.

Nouble joined League One club Plymouth Argyle on 3 August 2020.