If you and your neighbour want to build a fence on the line separating your land, you can share the construction and maintenance costs. You will also determine together the characteristics of this joint fence: its height, its color, the materials needed to manufacture it and the appropriate accessories.
Installing a fence precisely on the boundary that separates you from your neighbour remains the best way to interpret any ambiguities that could arise from the titles or the cadastre in your favour, even if you have to compromise on the characteristics of the fence. If you decide to install your fence anyway, and at your own expense, make sure that all parts of the fence are on your own property, even the concrete base buried underground. Also make sure that landmarks or stakes are always visible to avoid any confusion between the line imposed by your private fence and the actual boundary of ownership. Indeed, in the absence of bench-marks or boundary markers, the neighbour might end up believing that the fence corresponds to the property line. This is how the vast majority of property arguments get started.
To learn more about the installation of a dividing fence between neighbours, read this 2014 La Presse article
in which Benoît Péloquin is quoted.