Myriam has given good information, but another aspect to consider, and like Myriam I'm speaking of US law, is that The Livre" would only be descriptive as to businesses that deal in books, per her example.
If "The Livre" were used instead for a business related to, say educational services, or for perhaps a book-sized laptop, e.g., it would likely be considered not descriptive but "suggestive", putting it in a stronger position with regard to its use for similar goods/services. (And if it were used for a grocery store, it would be "arbitrary" and quite strong.)
But this is all assuming that you are using the mark for similar services to the existing user. Marks are taken in context. The whole point is to keep consumers from being confused as to the source of the services or goods by companies in similar businesses using similar names. Generally speaking, the more distinct your businesses, the closer your marks can be without infringement. The standard used to determine infringement here is "likelihood of confusion". Most countries take a similar approach, including Canada, it appears.
(Searching "marques de commerce" and "likelihood of confusion", I came upon this (1991) article from a Quebec firm,
THE ISSUE OF CONFUSION IN INFRINGEMENT AND OPPOSITION PROCEEDINGS: IS IT THE SAME? (ROBIC, Patent & Trademark Agents, Mtl., QC.), which you may find of interest. It appears to deal with the question of how confusion may be treated by the agency granting trademarks versus its treatment by the courts in infringement litigation, but may give you some helpful examples of the sorts of things considered.)
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Edit: I apparently didn't enter the above link correctly at first, so it wasn't working. It's fixed now.