Little is known about this young dark-skinned denizen of Paris; it is a fairly long time after his introduction before the reader even learns his name. (This wiki went with "Monsieur Andouille" in the interim.). He first appears in the comic well-advanced in his plot to overthrow the Master of Paris in (he thinks) collaboration with remote clank-puppeteer Drusus Beausoleil, who is revealed to actually be an official covert agent for the Master.
His personal symbol is a hand with an eye in the palm. Beausoleil is wearing it when he first appears on-screen.
Whatever his other faults, Du Quay is fairly restrained and rational as Sparky would-be conquerors go, displaying irritation at Beausoleil for proactively kidnapping Agatha and dragging her uninvited into his lair, and even posting a reminder to himself to take over Paris and leave it at that. "Don't get greedy!" He does accept Beausoleil's argument that Agatha might make a useful bargaining chip vis-a-vis a possibly-vengeful Gil if his plan goes off successfully. And the velvet dungeon is ready and waiting..
Said plan is thus: he has connected a scavenged piece of Castle Heterodyne (complete with a copy of the Castle's intellect) to a Telluric Wave Conductor and has ordered the resulting gestalt to subvert and take over all the thinking machines of Paris. When Du Quay somewhat unwisely leaves the two of them alone, Agatha is allowed by Beausoleil to tinker with this system as a test of her abilities. This gives her control of said system (and evidently all of Paris) when the Castle-copy immediately accepts her as The Heterodyne. (No blood test required, handy!)
Discovering this, Du Quay takes a shot at Agatha with his Death Ray, but Der Kestle hijacks the current Drusus clank to shield her from the blast. When the Castle patronizingly rejects his attempt at re-establishing control, Du Quay ascends to full level 3 laughing madness and activates a self-destruct mechanism that in theory will not only blow up his lair, but all of Paris. He is quickly subdued by Agatha by means of a wrench to the head, and the Castle casually deactivates the self-destruct. The Master then appears on the scene in person, equally casually cuts off Der Kestle's control, and prepares to arrest both Du Quay and Agatha. Thanks to a good word from Colette, Agatha is instead allowed an audience in the Awful Tower, but that's the last we see of Du Quay.
Du quay in French means of, by or from the docks. So this Du Quay's family might have been shipwrights or dockworkers at one time.