Drummond Tessier's marriage appears in the Ontario Marriage register:
Ref. 009 662, 1881, South Plantagenet
Drummond Tessier Age: 21 Residence: South Plantagenet Place of Birth: Cedres Bachelor Occupation: Farmer Parents: Leon and Lucie Tessier
Celina Martin Age: 15 Residence: South Plantagenet Place of Birth: Alfred Spinster Parents: Oliver and Elizabeth Martin Witnesses: Leon Tessier, South Plantagenet; Oliver Martin, South Plantagenet
Married, by banns, 10 October 1881 at South Plantagenet by J.O. Boucher
The 1881 census says that Drummond was born in Quebec, so his place of birth which he gives as Cedres (in 1860), would be Les Cedres (St. Joseph de Soulanges) which is just across the river from Beauharnois.
So you should be able to find his baptism, and his mother's surname in the parish register there. Alternatively, you should find the marriage of a Leon Tessier with a Lucie ? in the Drouin marriage dictionary. Keep in mind that "Leon" can be a short form of Napoleon, Leonard, Ponteleon etc.
The 1881 census also list Samuel (born 1854) and Marie Tessier living in South Plantagenet.