I'm working on a website for Canada which will have French and English versions. For SEO purposes, I would like to avoid using any language tag in URLs because I believe it will have more impact (e.g. example.ca/products better than en.example.ca/products or example.ca/en/products).

I believe this is technically possible because the2 languages are sufficiently different that the URLs won't be conflicting with one another (e.g. if you want a "product" page, it will be /products in English, and /produits in French so you know which language the URL is about).

Since Google (and most likely others) doesn't rely on the URL (nor HTML tags) to determine the content language I don't see any problems with search engines.

To make this possible I've thought about using a cookie distinct from the session cookie (e.g. example.org_language) with long term expiry (e.g. N years) that will memorize the language chosen by the user. That way when people visit the website with a new browser session, they get served the proper language.

I have already given up on users being able to switch one page from English to French: when people will chose English or French from the menu they will be redirected to the corresponding version of the home page.

Do you foresee any problems with not using a language component in the URL (whether domain or path)? (as long as one makes sure URLS don't conflict).