I'm planning an overnight visit to Reims from Paris, also in April. Here are a few notes from my research.
Martel (recommended to me by a Parisian friend) has tours daily, open from 10 a.m. to 1 p.m., and from 2.00 p.m. to 7 p.m. The last tour begins at 5.30 p.m. The tour lasts about an hour (though they have a couple of different tours). You choose how many tastings, up to 3. A tasting is about 1/2 glass. According to google maps, it's a 15 minute walk from Pommery, and 20 minutes from the Cathedral. The website says booking in advance is advisable.
Pommery is a 35 minute walk from the Cathedral (or a 6 minute drive - take a taxi). It's also open daily. There are different tours. Book in advance.
Taittinger is a block or two from Martel (250 m.). Their website doesn't work.
Lanson was recommended to me by someone on the forum as a smaller house. The website is mostly in French. Lanson
You can book through the website. They are open Monday-Friday from 10-1 p.m., 2-7 p.m. It's about 30 minutes on foot (or a short taxi ride) , but not near the other houses or the Cathedral.
Mumm I combed through their website but could not find any prices. It's a 15 minute walk from the Museum of the Surrender mentioned above (Musee de la Reddition).
All the walking times are from Google maps.
Trains from Paris leave from Gare de l'Est. There are trains that go to Champagne-Ardenne where you transfer to the local TER train to Reims and trains that go to Reims-Ville. While it's more convenient to take the Reims-Ville train, it may fit your schedule better to take the Champagne-Ardenne train. Use this site https://www.capitainetrain.com/search/ to see schedules and book tickets.