He was born in Montreal in 1785, the son of Joseph Quesnel, and studied at the Collège Saint-Raphaël. He articled in law with Stephen Sewell, was admitted to the bar in 1807 and set up practice in Montreal. Quesnel also invested in the fur trade and speculated in land. He served in the local militia during the War of 1812 and reached the rank of major in 1830. He represented Kent County, later Chambly, in the Legislative Assembly of Lower Canada from 1820 to 1834. Quesnel opposed the union of Upper and Lower Canada proposed in the early 1820s. In 1831, he was named King's Counsel. He was a moderate Reformer and opposed such measures as an elected legislative council and did not support the Ninety-Two Resolutions. He was named to the Executive Council in 1837 and continued to opposed the union of the two Canadas. After that union came to pass, he was elected to the Legislative Assembly of the Province of Canada in 1841 for Montmorency; he was defeated in 1844. Quesnel was named to the Royal Institution for the Advancement of Learning in 1845. In 1848, he was appointed to the Legislative Council and served until his death in Montreal in 1866. He supported the 1849 Rebellion Losses Bill and opposed annexation to the United States; he ensured that proper compensation for seigneurs was built into legislation to abolish seigneurial tenure. Quesnel was elected president of the Saint-Jean-Baptiste Society of Montreal in 1860. He was also a director of La Banque du Peuple and served as its president from 1859 to 1865. He was buried in the Notre Dame des Neiges Cemetery.
His brother Jules-Maurice Quesnel worked in the fur trade and also served on the Legislative Council.