According to Jewish law, if his mother was Jewish, then so was he.
The concept of a "half-jew" is modern invention, and not accepted by orthodox Jews
I know, I'm not talking about half-jews at all; if I make up a religion stating lizard aliens identify their descendants with the name Leonardo, does that make him a lizard alien? According to me, yes, but that doesn't change at all who he was.
Also,that might be an unpopular point of view, but unless he was raised in the Jewish culture, he wasn't Jewish even if the claim was somehow true. Perhaps ethnically half-Jewish.