After a sole season in the French league with Olympique de Marseille, Boghossian moved to Italy, and played in Serie A with S.S.C. Napoli, U.C. Sampdoria and Parma F.C., where he had his most successful years, alongside compatriot Lilian Thuram.
An international since 1997, Boghossian won the 1998 World Cup with France, but was injured the day before Euro 2000 started. He also appeared at the 2002 World Cup, and in total made 26 international appearances, scoring 2 goals.