From that site: "Ste Catherine is the patron saint of single girls" Ah. That explains a lot. Particularly in Canada apparantly. So that's who the 'brothers' are. A lament for unmarried girls - but a jokey one.

I wonder why Kirsty MacColl has changed the first line from
Moi, j'me promene sous Ste Catherine to ... sur Ste Catherine
(I'm walking under the street / ... on the street.)
I've always thought this is about staying below ground in Montreal in the winter, and that it was what the locals all did.

This page (in French) provides more illumination, in particular that it may also refer to Kate (Catherine) McGarrigle.

And I suspect that 'fait d'la politique' doesn't literally mean 'in politics'.