A look in any encyclopaedia or history book will show you that Franz Ferdinand and his wife Sophie Chotek had three children. These were Sophie (1901-90), Maximilian (1902-62) and Ernst (1904-54). All three remained in Europe after their parents' assassination in Sarajevo. Furthermore, the family did not renounce the throne. Rather Franz Ferdinand's marriage to Sophie was a morganatic one, which stipulated that none of his children would inherit from him or be in line for the imperial throne.
Rather than chasing family stories of royal ancestors, I would suggest you try and locate reliable data on your parents and grandparents first and see where that will lead you.