Called to the bar in 1904, Montpetit worked as a lawyer and taught political economy before he obtained a scholarship in 1907, which made him the first holder of such a scholarship to be officially sent by the province of Quebec to Paris. In Paris he studied political and social science, receiving a degree in both. He founded the École des sciences sociales in 1920, which he then ran.
Between 1920 and 1950 he was active at the Université de Montréal, where he was secretary general, dean of the faculty of social sciences, member of the senate and member of the board of direction. He taught at the business school affiliated with the Université de Montréal, the École des hautes études commerciales (HEC) from 1910 to 1939, as well as at the university's law school, from 1910 to his death in 1954.
In 1967, a monument to Montpetit was unveiled on the Université de Montréal campus and the name of nearby Maplewood Avenue in Côte-des-Neiges was changed to boulevard Édouard-Montpetit. The name of Maplewood Avenue in Outremont did not change.
A partial list of Montpetit's published works includes:
- Au service de la tradition française (1920)
- Pour une doctrine (1931)
- Les cordons de la bourse (1935)
- Le front contre la vitre (1936)
- La conquête économique (1938–1940)
- Reflets d'Amérique (1941)
- Propos sur la montagne: Essais (1946)