Is Picard Wesley's father?
No.
. . .
I don't see any reason to think so, really. Yes, Beverly seems keen on Picard being a role model or father figure for Wes, but that is really not even evidence in favor of the theory. Beverly respects J-L highly, and this "I have something to tell you" is really, IMO, nothing more than that she has feelings for him. It would take all the way until "Attached" for it to become clear that it is mutual. I really don't think anything ever happened between Bev and J-L other than they both took a couple of long looks at each other from across the ballroom.
No.
. . .
I don't see any reason to think so, really. Yes, Beverly seems keen on Picard being a role model or father figure for Wes, but that is really not even evidence in favor of the theory. Beverly respects J-L highly, and this "I have something to tell you" is really, IMO, nothing more than that she has feelings for him. It would take all the way until "Attached" for it to become clear that it is mutual. I really don't think anything ever happened between Bev and J-L other than they both took a couple of long looks at each other from across the ballroom.