This question is a blend of star-trek and story-identification because I am not sure if Picard is referencing something in-universe (ie - something specifically within Star Trek history - like Zefram Cochran) or in the 'real world' (ie - Picard referencing Charles Dickens)
In the Star Trek: The Next Generation book Armageddon's Arrow, a character states that Picard has been reading a book - described thusly:
"The one with the aliens who crashed on Earth a long time ago..it's a big secret, and everybody's looking for them and worried that more aliens will come, but there are these people who are nice and who are trying to help them get away."
What book is Picard reading?
(while it sounds like it could be the plot to the DS9 episode Little Green Men, it seems unlikely that that event would be novelized and read by Picard to the character that is speaking.)