Rousset started his career with Sochaux in 1982, where he spent eight seasons, playing more than 100 times for the Montbéliard side before he was transferred to Olympique Lyonnais in 1990.
He quickly established himself as the first choice goalkeeper at the Stade de Gerland, playing 98 matches over the next 3 seasons.
In 1993, Rousset was surprisingly transferred to Olympique de Marseille, who were the reigning European Champions but embroiled in a corruption scandal.
He spent six seasons in Edinburgh, helping transform a Hearts side that had flirted with relegation into a dominant domestic competitor that came very close to splitting the Old Firm.
He also won his only major honour there, the Scottish Cup in 1998, having been a losing finalist on 3 previous occasions earlier in his career (1988 with Sochaux and twice in 1996 with Hearts).