‘Le Midi’ is used here, just as le Sud, or l’Est etc to refer to a ‘region’.

 Le Canal du Midi - The Canal of the Midi. 

Thanks, makes sense,  sort of like how in French it is "Les 24 Heures du Mans" since the name of the town is Le Mans not Mans,  which in English gives us,  "The 24 hours of Le Mans"  

Canal du Midi -- Channel of the South
Canal de midi -- South-channel