it seemed like an idea they were going to run with then backed away from. In the end it was better to let the Traveller abduct him on a gentleman's vacation of the other side of the Galaxy.
I like to believe Picard ultimately started flowing like a river because of those deaths, which triggered a loss of past, midlife crisis of sorts, and a slew of other personal issues that all culminated at just the worst possible time, so he chooses to focus just on one issue when Troi comes in to tell him and the audience the obvious. Wesley could have been a stepson, but actual offspring? I never got that vibe. It's not a bad notion, but with the amount of backstory, even in the kinkiest season 1 story, it just doesn't work. BTW: Best avatar from anyone!
Hey now, maybe we're on to something. So, Wesley is a Picard, quits Starfleet and ends up on Earth with the other Picards and burns to death in a fire, thus solving the Wesley problem once and for all.
I have to say in regards to the reasoning of Picard getting so emotional about Rene's death being because he is the father is false for three reasons. First, as someone stated before, he was the last child to carry the Picard name, and that was something that hit him hard because he always figured with Rene, the line can go on. Second, Picard recognized a lot of himself at that age. Rene was always dreaming of adventures in space, and Picard was even trying to get Robert to let him have those dreams. Third, just because someone is not your own child doesn't mean you are not going to be devastated if that child is gravely injured or dies. I have no kids, but I am close to my wife's niece and nephews, particularly the older nephew. If something were to happen to any of them, I would be completely devastated. Love doesn't stop with your own bloodline, and to think or say otherwise says more about that person than the responses it might incite.