He was born in Memramcook, New Brunswick, the son of Allain Landry and Anastasie Dupuis, and was educated there. His mother was a descendant of Charles de Saint-Étienne de la Tour who had been governor of Acadia. Landry taught school for a time. He married Pélagie Caissie in 1839. He was defeated by William Crane in 1850 but was elected in a by-election held in 1853 after Crane died. Landry opposed Confederation and railway construction, viewing both as not benefiting Acadians. He died in Memramcook at the age of 71.
His son Pierre-Amand served in the provincial assembly and the Canadian House of Commons.