I could be wrong; however, I am reasonably confident to put my thoughts in writing.
Off course, your parents were born in Ithaki, Greece, and off course they lived there for quite a few years.
However, assuming you spelt the name correctly, I believe you are a descendent of a French family, that dates back well over 1000 years. Probably Normans, they were the owners of Chateau (Castle) de Condrieu (De Condrieu = Decondris).
Your family records are probably kept in Venice.
If I am right, it is worth searching for the truth.