According to Wiki, it is not a French word, but a French corruption of a Miami Indian word. Nasty cultural appropriation. The city must change its name now.
And while we’re at it, the Rev. Dukes has a name that is all too close to David Duke’s, and is itself derived from an ancient Latin term implying patriarchy and bringing to mind various anti-pacifist traits..
Your description is more precise, however I was just posting the shortcut. Chicago comes via the French corruption, not the orginal Algonquin source.