As a rule of thumb, schools discourage students from taking an exchange if they need to find a job. That's one reason why the exchange generally happens after the summer internship: students with offers can take the exchange, leaving the careers team to focus on fewer people. Very few schools (Chicago, Insead, Harvard etc) have careers staff focussed on supporting job hunts in other countries. On my exchange, I found the careers team were polite but always put their own students first. I got a great review of my resume. I was able to access the alumni database while a student. I could attend most, but not all, events organized by the careers team (often only when not enough of the home-school students wanted to attend).
You also have to consider the visa situation and the domestic market. Canada loves foreign talent because it can be paid a discount. The USA doesn't. UK recruiters know what an MBA is; many French ones don't.
Stuart, could you explain the part where you say foreign talent can be paid a discount in Canada, but not in US. And how that translates to the markets in the UK and France too?