According to a very nice gentleman at the Algerian Embassy in Washington, D.C. whom I rang up on the phone just now, the name means "a birth". He had to ask a few other people in the office, and he kept referring to the athlete just by the name of "Zindane". So I'm not certain if this is the actual meaning of "Zinedine".
Hey, Pav... How come I couldn't find an Algerian Embassy for Greece? I just looked right now on http://www.embassyworld.com/
I was going to suggest you try ringing up the Algerians there in Greece, to compare their info to what I'd gotten.