No, he's not the son of 007, but James Bond, Jr. was, in fact, the nephew of Ian Fleming's iconic hero.
In 1991, United Artists recruited the staff at Murakami-Wolf-Swenson (Teenage Mutant Ninja Turtles) to produce James Bond, Jr. as a daily series, hoping that the next generation of Bond would resonate with his peers in the audience. Sad to say, he didn't. The series lasted one season, even though it had the usual merchandising tie-ins, such as toys and comic books.
Here's the series premiere, "In The Beginning":
I wanted to like this show, since I'm a Bond fan myself, but I couldn't get into it. Locally, the show aired in the morning before I went off to work, which didn't give me much of a chance.