People are always remarking (at least, fans of Deep Space Nine are always remarking) that it seemed to take several seasons before Benjamin Sisko actually became a functioning character. Well, one of the reasons that the first season of Next Generation can be so painful is that Jean-Luc Picard had the same problem.
Sure, he had backstory. He had a previous command, lost it in battle to the then-mysterious Ferengi. Conceptually, he was obviously supposed to be completely different from Kirk. He was older, more cerebral, and definitely could not be mistaken for American. (William Shatner, it might bear repeating, is actually Canadian, and so is definitely not from Iowa.) Though Patrick Stewart is very much British, Picard was meant to be French. It there in his name. In initial episodes, Picard even tries to be the French equivalent of Chekov's Super Russian. (It's not until Star Trek Nemesis were Picard technically being French is at all relevant again, besides his family interest in wine.)
"We'll Always Have Paris" is the first sign that Picard was maybe more like Kirk when he was younger than viewer might originally have suspected. (And actually, later developments all but prove that when he was younger he was actually worse than Kirk, but we'll cross that bridge when we reach it.) It's also an episode that again would have had a great deal more significance if the show hadn't changed or lasted quite so long. What I'm saying is that, like Kirk in Wrath of Khan, Picard runs into an old flame, and complications ensue.
So few romantic stories were ever developed for Picard that on that score alone "Paris" will forever been in some way memorable. It's a cheap knockoff of Casablanca (the Deep Space Nine episode "Profit and Loss" has a similar claim and is more memorable), and not very convincing as far as the Picard we know to this point, or really at any other point.
The problem is that this old flame has since very much moved on, in quite a different way than Picard. She's gotten married, and is here because of one of those Federation science projects that in a very typical way for this series goes horribly awry (the only thing that's memorable about it is when there's a bunch of Datas standing around in the same room, but "A Fistful of Datas" make a more memorable image of even that).
In the end it comes off as another attempt to pass the obviously British Picard off as French. His brother Robert is the closest we ever come to finding out how Picard ended up the way he did. "We'll Always Have Paris" becomes a novelty before long, an experiment that does not quite succeed. You think you know Picard? Well, not yet.
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Memory Alpha summary.