John, please tell us if this is your first trip to Europe, or your first time on a train in Europe. There are some useful general guides on our host's site, top left:
https://www.ricksteves.com/travel-tips
In general, you do have to change stations (St. Lazare to Nord) in Paris for this route. You can get an idea of your trip with the SNCF website, https://www.sncf-connect.com/en-en/ It looks like the shortest trip is 4h:30m, but that includes an hour for the transfer in Paris. Is your daughter in Brussels, or a nearby city? I partly ask because Thalys/Eurostar only goes to one of the three "downtown" stations in Brussels. But all international tickets include the right to take a local, unreserved, non-First Class train from Brussels Zuid/Midi to either of the two other stations.
Eurostar is much more likely to have upscale accomodations, if that is important to you. So it might work better to deliberately buy two tickets. I don't personally know if Eurostar has an obligation to you if SNCF fails to deliver you to Paris in time for your reserved-seat only Eurostar ticket. Of course there are conventional trains to Brussels, but they are slower and less luxurious. (I take Eurostar all the time, I'm not making fun of your First Class request!) I can't predict how hard it will be to purchase different classes of service on two trains that don't offer precisely the same classes, if you see what I mean.
Do you have a way to print out a bar-coded ticket (or two) today? That's a comforting reassurance that avoids waiting to buy in Paris. Other people use phone Apps, but that's too modern for me!
Considering that it's international, involves a special service train, and is at holiday time, this is not a bad train trip.
