Frenette succeeded Frank McKenna as premier when McKenna stepped down and the Liberal party required an interim leader.
He served as premier for seven months until Camille Theriault won the Liberal leadership race in May 1998.
Frenette says Gallant has what it takes to be the next premier of New Brunswick.
There are two other candidates in the leadership race: farmer Nick Duivenvoorden and Moncton lawyer Mike Murphy, who served in the cabinet of former premier Shawn Graham.
The leadership convention is at the end of October.