One of the most interesting things about captain Picard is that he says he's not good with kids. In the first episode he literally asked Riker to keep kids away from him. However, when Picard actually has to deal with kids, he's not half bad at it.
Like when he has to deal with a kid he's awkward, sure, but doesn't immediately brush them off. Like that one time a little girl asked door uppies, he picked her up, even though he was visibly uncomfortable.
In Distaster he managed to keep three little kids calm while they all were stuck in a turbolfit.
Or when in Suddenly Human he was supposed to take care of the human kid they found on an alien ship and wasn't half bad at it either. Was he awkward? Yes. Did he get stabbed? Also yes. But attempts were made and were quite successful.
He's got pretty good relationship with his nephew. That scene when he plays along with him being uncle was adorable. I wish we'd see more of him with Rene, it's so cute 😭
He shares things with Wesley he never told others, like not getting into Starfleet Academy at first attempt. They grew closer throughout the series, I think The Last Mission is a good example of how their relationship developed. Also Wesley himself said Picard would make a great father.
Whenever Data needs help while he's being confused by human things™ he goes straight to Picard. I think Picard kind of thinks of him as his kid too.
He regularly came to hang out with Elnor during Romulan Evacuation, who, keep in mind, was very little at the time.
We also saw a picture of him holding little Thaddeus Troi-Riker, and was even smiling (could be for the picture though, but his growth over the time showed he slowly started feeling more comfortable with children). And let's not forget about episode Bloodlines, in which he was convinced he had a kid and tried to bond with him (it worked out in the end though, so I'm calling it a success).
There's definitely some level of awkwardness while he's with younger kids, sure. There are several other cases when he has to deal with smaller children and we see that he just doesn't seem to know what he's supposed to act like around them.
In my opinion he's like that because he himself didn't have good role model as a kid and either isn't sure how to act or believes that he won't be able to act differently from his own father, so just thought it'd be easier to just avoid children altogether. Well, that didn't exactly work out, did it's, cap?
I couldn't help myself but to put that photo in here 😂 beginnings sure we're awkward
Anyway, I think that Picard secretly longs to have a family, as we've seen in Star Trek: Generations (the Nexus, you know, the same thing that makes your dreams come true?), so it leads me to believe that when in response to the Jack's question about family when he said "Starfleet is the only family I need" didn't mean Starfleet as the organization but it just people who he considers family happened to be in Starfleet.
