As it turns out, the English word canopy stems from the same French word. Whereas Greek καναπές retained only the 'couch part' of the original French meaning, canopy retained the other half, denoting "a covering or hangings suspended over a throne, couch, bed, etc." (Oxford English Dictionary). But it did not retain the idea that this "covering" is a κουνουπιέρα, i.e. a mosquito net, thus also losing the connection to the etymological root κώνοψ/mosquitio.
It is noteworthy that according to the OED canopy and its French predecessor (and therefore also καναπές) have their origin in the Ancient Greek word κωνωπεῖον - already denoting "an Egyptian bed or couch with mosquito curtains". This in turn derives from κώνοψ, as Vassilis3 has already mentioned above.