can you take a train from gare de lyon or Gare de Nord to Reims

Why does it have to be Gare du Nord or Gare de Lyon? Trains toward the east leave from the Gare de l’Est. Loads of trains toward Reims from there though.

Trains really do not pass through Paris. Gare de Nord (North) services trains going north, others for east and west, There is something like 17 train stations in Paris so you need the station that services train headed in the direction you want to go. I will check the schedule.

Here's why there are so many different terminal stations, all going in a different directions out from Paris like spokes on a wheel. Different companies created train lines that went in different directions in the 19th century. All these different train lines were independently owned. They were all united later into one company. So if you want to go east to Reims, you catch the train at Gare de l'Est. Est means east in English.
Trains from Gare de Lyon go to Lyon and on south to Marseille and Nice.
Trains from Gare du Nord go north to Brussels and Amsterdam.

If you want the bus from Bastille (per your previous post) to Gare de l'Est, take the 91 bus.

When planning train trips on www.sncf-connect.com just select "Paris (ville)" in the from field. That way you can let the system select the correct terminal for you.

When France started building railways the government literally carved up the country in segments, with Paris in the middle. Like you would cut up a pie.
And each segment was then given to a different company. They then all build their own terminals. They added two other sectors: From the Med to the Rhine, and from the Atlantic to the Med, and thus ended up with 9 companies. Until those were all absorbed in the SNCF.

Trains are not buses that can go wherever. Tracks are fixed; different stations in Paris which is the rail hub of France serve different regions and countries. So you cannot pick your station, your choicer of destination chooses for you. That is why when booking you enter Paris not a station and the site will assign the station that is used. There are some routes where there is more than one station -- they will show up in the search for trains. But you can't pick your station, the destination picks your station options.

Imagine how sad it would be to have Paris' lovely ambience disturbed by tains crossing the city! Thank heaven for the various stations. Just a fun fact......When the Musee d'Orsay was the Gare d'Orsay it used to serve southwest France. It was "decommissioned" as a train station because its fixed tracks were too short for the newer, longer trains that came into use in the 1930's. How wonderful that it was turned into the museum, and that the beautiful clock was retained!