Bah, this isn't true, not at all.
I work as a section head in National Defence. Up until two years ago when the layoffs began, we hired about 10 people a year in my section and a second peer section we work closely with. Now we hire 1-2 a year and that will continue another two years or so when we expect growth to resume.
In this department less than 50% of jobs require some sort of bilingualism. The senior ones mostly do, but that's ok because you can get training as a junior employee. Even those jobs that do require french, few require you to be actually bilingual.
Seek out departments that do not interface with the public, or ones that do not do most of their work in Ottawa or Quebec. Far less bilingualism in those departments. DND, CSE, Fisheries, Coast Guard, Agriculture, things like that. Stay away from the ones that deal with people all the time (CRA, Customs) and ones that deal with inter-governmental issues (PWGSC, Privy Council Office).
Just my two cents. I don't speak a lick of french and about half of my colleagues are the same.