I think what you said is slightly wrong. Island and isle are both English words that seem to have no ethymological connection. However close semantic relation of “isle” might have cause the introduction of the “s” at some point. Isle itself probably comes from latin “insula”. The French still have only one word “Île”. Germans have “Eiland” and “Insel”.

island [OE] Despite their similarity, island has no etymological connection with isle (their resemblance is due to a 16th-century change in the spelling of island under the influence of its semantic neighbour isle). Island comes ultimately from a prehistoric Germanic *aujō, which denoted ‘land associated with water,’ and was distantly related to Latin aqua ‘water’. This passed into Old English as īeg ‘island,’ which was subsequently compounded with land to form īegland ‘island’. By the late Middle English period this had developed to iland, the form which was turned into island. (A diminutive form of Old English īeg, incidentally, has given us eyot ‘small island in a river’ [OE].)

Isle [13] itself comes via Old French ile from Latin insula (the s is a 15th-century reintroduction from Latin). Other contributions made by insula to English include insular [17], insulate [16], insulin, isolate [via Italian) [18], and peninsula [16].