Nouma started his career in the Paris Saint-Germain youth team before moving around other teams in France. He played for Lille and Caen before moving back to PSG for two seasons in 1994. He helped PSG win both the 1994–95 Coupe de la Ligue and the 1994–95 Coupe de France, playing as a substitute in both finals, the latter against future club Strasbourg. He also scored as PSG won the 1995 Trophée des Champions. In 1996 he left for Strasbourg, winning the Coupe de la Ligue there in 1997 and staying for two seasons, before moving to Lens. While at Lens he played in the final as they won the 1998–99 Coupe de la Ligue, which was the third time he’d won the trophy in five seasons and with three different teams.

After two seasons at Lens, he left for Turkish club Beşiktaş, where he achieved phenomenal success and still maintains his popularity among Beşiktaş fans, who composed special songs for him. He played for them for one season before moving to play for Marseille the next year. He returned for a short spell at Beşiktaş the next season, but received a seven-month suspension for celebrating a goal against arch-rivals Fenerbahçe by putting his hands down his shorts, a gesture he described as “a private moment of joy”. The Beşiktaş board were forced to cancel his contract as a result. The incident did not diminish his popularity with Beşiktaş fans, who still look back fondly on his lob shot against Dynamo Kiev in the third round of the UEFA Cup in 2003.