French Europe Minister Harlem Desir called the move "scandalous" and said it raised questions about the EU's conflict of interest rules.
Ex-commissioners are free to take up a new role 18 months after leaving.
Despite accepting the job after 20 months, Mr Barroso has come under fire for ignoring the spirit of the rules.
Mr Desir drew attention to the ill-timing of the job with Goldman Sachs.
