The words island and isle are not cognate. Really.
Island derives from an Old English word, iegland.
Isle, by contrast, is from Old French, probably an evolution of the Latin insula. It was only later, well after the Norman invasion of England, that people got confused by the two and the s snuck away from isle and stowed away on island.
That s was kind of promiscuous. It also hooked up with the Old French word ele – bird’s wing, side of a ship, ultimately from Latin ala/axilla/axis – and gave us the modern English word aisle. Again, because people got confused. I blame our public schools…