After finishing 2nd place in the 1993 Formula Renault Eurocup, Marseille-born Minassian graduated to the French Formula Three Championship where he finished runner-up to countryman Laurent Redon at his second attempt in 1995.

He graduated to Formula 3000 with West Competition for 1998, but failed to impress whilst his teammate Nick Heidfeld mounted a strong challenge for overall honours.

The following year, he moved to Kid Jensen Racing where he enjoyed more success, including an emphatic lights-to-flag triumph at Silverstone.

He signed for the illustrious Super Nova Racing team in 2000 where he came a strong 2nd in the championship.

Unable to secure a Formula One drive, Minassian drove in 2001 for Target Chip Ganassi Racing with F3000 title adversary Bruno Junqueira in CART and competed in the Indianapolis 500 before being released by the team.