OK; however, even with this canal being built on schedule, Louis (either the 13th or the 14th) can relocate the French capital to Orleans and then aggressively promote trade and travel on this canal between Paris and Orleans.
From the XIIIth century onwards, Paris as a capital is far too entranched into French political identity to be written off, especially in favour of a city as exc entered as Orléans (especially giving the recent Protestantism of the city) : distance are still too important (at best 4 hours of uninterrupted travel for
malle-postes in the XIXth, more in
dilligences). it's worth noting that before the XVIIIth century, most of this traffic was focused on northern France.
You'd need a major political identity shift, for writting off Paris as a capital from there(remembering that centralization, politically and administratively, was a pluricentury project) : keeping in mind that even French Revolution, which was as much as a radical identitarian shift you could get, never really put that in question (partially because of the existence of Versailles as a political center).
Remember that, at this point, virtually every regional urban or structural project was made, including Paris as a natural center : any capital change this radical (again, not that you couldn't end with a La Paz/Sucre situation, on which Paris would still have the upper position IMO) would need a massive update of northern France urban and structural policy.