The answer is that it depends on Province.

It seems that Quebec is particularly strict here, with Microsoft losing a battle to use the term "Engineers" over two decades ago, https://www.canadianconsultingengineer.com/quebec-order-of-engineers-wins-legal-battle-with-microsoft/

Similarly, it seems there was a lot of activity a couple of years ago in Alberta to protect the term as per https://edmonton.taproot.news/news/2022/10/17/tech-leaders-seek-easing-of-rules-around-software-engineer-designation - with the result that the law is being changed to explicitly exempt "software engineer" from protection as per https://globalnews.ca/news/10084623/engineers-canada-urges-alberta-to-reconsider-change-to-rules-around-engineer-title/

In Ontario specifically - which is the most populated province of Canada - my layman's reading of https://www.ontario.ca/laws/statute/90p28 12 (1),

When licences or certificates required

Licensing requirement

No person shall engage in the practice of professional engineering or hold himself, herself or itself out as engaging in the practice of professional engineering unless the person is the holder of a licence, a temporary licence, a provisional licence or a limited licence.

Similarly, looking at https://www.ontario.ca/laws/statute/s10016 5(1)

“practice of professional engineering” means any act of planning, designing, composing, evaluating, advising, reporting, directing or supervising that requires the application of engineering principles and concerns the safeguarding of life, health, property, economic interests, the public welfare or the environment, or the managing of any such act; (“exercice de la profession d’ingénieur”)

And from https://www.peo.on.ca/public-protection/complaints-and-illegal-practice/report-unlicensed-individuals-or-companies-2#software

where use of the software impacts the health, safety or property of its users. PEO considers non-licensed use of “Software Engineer” to be a violation of our Act.

But most software development is not, for example, directly related to health & safety.

Basically in Ontario it seems "professional engineer" is the main regulated term, and "engineer" is only restricted in a subset of limited cases. (Note that this might be a relatively recent change though - the Professional Engineers Act is dated to 1990, but the Open for Business Act from 2010 made a number of changes to it. And it's specific to just Ontario.)

Edit: Now it seems that the Ontario branch of Engineers Canada, Professional Engineers Ontario, isn't quite happy with this state of affairs. They make their case here, https://www.peo.on.ca/public-protection/complaints-and-illegal-practice/report-unlicensed-individuals-or-companies in the "Software engineering and misleading certifications" section near the bottom:

PEO has taken action against the use of the term "engineer" by several software companies. PEO negotiated with Banyan Systems to revise its training materials to replace the term "Certified Banyan Engineer" with "CBE". PEO also requested that Microsoft Canada Inc., replace the terms "Microsoft Certified Systems Engineer" and "Microsoft Certified Professional Systems Engineer" with alternate terms that do not use the word "engineer", to avoid violating the Professional Engineers Act and trademark legislation.

On July 25, 2002 Microsoft Canada announced that they will continue to use the term 'engineer' as part of the Microsoft Certified Systems Engineer (MCSE) designation.

The rest of the page is just about how to report misuse of the "professional engineer" term, e.g.

use the title "professional engineer" or an abbreviation or variation as an occupational designation

It's quite telling then that the vast majority of jobs in Canada with the title "Network Engineer" are for companies based in Ontario, at least looking at https://ca.indeed.com/q-network-engineer-jobs.html?vjk=4d0293c813a90300

There are other cases of courts declaring engineering to be unprotected, see for example https://www.smartbiggar.ca/insights/publication/canadian-council-of-professional-engineers-fails-to-prevent-registration-of-engineering-mark