Former Ottawan here.
Salvation Army & Saint Vincent de Paul are both church based thrift stores. Don't overlook the SVdP in Hull/Gatineau on Eddy St.
Value Village is connected to the Diabetes Foundation but also has a mission to train the unemployed for the workforce. Both stores I know are suburban. A car is necessary.
Goodwill exists in a small way.
In Ottawa there is a United Church on Elgin St. with a good thrift store.
There is also Ottawa Neighbourhood Services, which is also a job training outfit, but it is chaotic and deep in the suburbs.
In French some of these would be called:
Armee du Salut
Village des valeurs.
Used in French is 'd'occasion' so magasin d'occasion. Vintage is 'friperie".
In Montreal, if you can try to speak French a little, most polite people (and those who love their language) will quickly switch to English if only to spare themselves the pain.