If you look are in most dictionaries, the word secure originates from the Latin words se-(without) and cure (care). But I am not convinced. The word sure in Italian originates from the same word sicuro or securo.
The Greek word is for the word sure is σίγουρος and it very much is listened the same way as sicuro.
So for me it is more logical that the first use of the word is sure that originates from the Greek word σίγουρος (siguros) and because of the meaning it became secure.