Chollet began his political career as a municipal councillor in Agen in 1977.
Four years later, he became deputy mayor and became General Councilor of the Canton of Agen-Centre [fr] in 1981.
He was elected mayor of Agen in 1989 and resigned as General Councilor due to the law prohibiting certain dual mandates.
He was president of the Amicale des maires de Lot-et-Garonne from 1989 to 2001.
In 1986, Chollet was elected to the National Assembly, representing Lot-et-Garonne through proportional representation.