I think René Picard was Jean Luc's son.

Consider also the way Picard was around children.

Encounter at Farpoint

PICARD: Using the same kind of strength you showed with Captain DeSoto, I would appreciate it if you can keep me from making an ass of myself with children.
RIKER: Sir?
PICARD: I'm not a family man, Riker, and yet, Starfleet has given me a ship with children aboard.
RIKER: Yes, sir. PICARD: And I don't feel comfortable with children. But, since a captain needs an image of geniality, you're to see that's what I project.

Suddenly Human

PICARD: You're probably not aware of this, but I have never been particularly comfortable around children.
TROI: Really?
PICARD: For some reason, they just don't seem to respond to me.
TROI: I see.
PICARD: Frankly, I think my time would be best served carrying out the duties and responsibilities of a Starfleet Captain.
TROI: Seldom have I heard an explanation so well-rehearsed.
PICARD: Look, Counsellor, I just feel that I'm not the right person for this job.
TROI: Strange, isn't it? You'll travel light years, dodge asteroid storms, brave hostile aliens, and yet when asked to assume a parental role, you cringe. Why do you suppose that is?
PICARD: I'm not cringing. I'm just acknowledging my limitations.
TROI: When you were a child, did you have any friends? Other children you played with?
PICARD: I don't think that has anything to do with anything. Well, perhaps it was because. This is foolish.
TROI: What were you going to say?
PICARD: it's just that ever since I was a child I've always known exactly what I wanted to do. Be a member of Starfleet. Nothing else mattered to me. Virtually my entire youth was spent in the pursuit of that goal. In fact, I probably skipped my childhood altogether.

The Inner Light, after an entire alternative lifetime

PICARD: I would have believed I didn't need children to complete my life. Now I couldn't imagine life without them.

and everything in Disaster.

Then consider Picard's attitude in Generations, in the nexus, AFTER Rene's death.

/r/DaystromInstitute Thread