He was born in Béarn, and served as syndic for the region, then served as jurist for the Parlement of Paris. He became a Freemason and a member of the Jacobin Club, making himself known as an adversary of the deputies from the colonies, and a partisan of Jacques Pierre Brissot and Léger-Félicité Sonthonax. A prosecutor for the Revolutionary Tribunal, he joined the Commune, and became a member of its General Council.
Arrived in Le Cap aboard the America as a Civil Commissioner to Saint-Domingue on 17 September 1792, along with Sonthonax and Jean-Antoine Ailhaud. Polverel was given charge of the West, and when Ailhaud abandoned his post, he took responsibility for the South as well.
Although his more famous colleague Sonthonax is usually given full credit for this achievement, it was Polverel who wrote his own set of laws governing post-emancipation plantation labor, different from those established by Sonthonax; these remained in place under the rule of André Rigaud until 1800. All laws were written without French overseeing, and the National Convention conceded to accept them. They also demanded that all freed slaves continue to work on the plantations.
Although France confirmed the end of slavery on 4 February 1794, emancipation was controversial, and virulently opposed by Maximilien de Robespierre; the two Commissioners were recalled to Paris. Polverel faced being guillotined, but Robespierre's fall occurred before a decision could be taken. He died there in Paris before being exonerated.