DNA testing has proven the Da Vinci Code stuff (with Jesus' family becoming a line of French aristocracy) all fiction.
But there is strong cultural evidence that Jesus had a wife and kids. What is this cultural evidence? It's just that to be a Jewish man in those times, at that place, meant you HAD to. You weren't given a choice. Even if you were an obvious huge girly pansy, too bad, you had that marriage, they all made sure of it. No choice.
If kids didn't come out of the marriage, because someone was barren, a HUGE deal was made of it. These things were very big deals at the time. If he somehow wiggled out of it, a HUGE deal would have been made of it, and everyone would have never stopped making a big deal of it, since it would have been such a monstrous aberration to the society. He would have been like an "outlaw" and he was never called anything like that.
In fact, he was called Rabbi by his own people, and to be called that you HAD to have a wife and kids. Or else you just don't get called that.
The Syrian Orthodox Church assumes they come from Jesus' earthly family. So this isn't a new radical idea. The Syrian Orthodox Church is as old and conservative as you can get, regarding this matter.