That's a great question, Len! I would just try some of the local wine shops, many of which have free tastings (although I think in exchange you're sort of expected to buy some wine).
I know Caves Augé has them and if I'm not mistaken......so does Le Repaire de Bacchus on the Rue Montorgueil which is one of the best streets in Parirs. The ones at Le Repaire, I believe, are less formal--like maybe you just catch them on a good day (I'm almost positive I remember reading that this is Patricia Wells's favorite wine store). Generally speaking, wine merchants in Paris LOVE to chat about their stock so you can probably just approach one and ask about their wines, provided you make it clear that you're willing to purchase some. I've never been here, but I do know there's a wine museum, Musée du Vin and I'd bet money they have tastings.
It's possible to take a day trip to Reims by train from the Gare SNCF de Paris Est station. Travel time is around 48-73 minutes. A quick look at the Rail Europe site yielded a round trip fare on June 18 for $63. The Office de Tourisme - Gare, about 1km (.6/mile) from the train station, is next door to the beautiful Cathédrale Notre-Dame de Reims. They could give you a map and direct you to Champagne cellars that offer tours and tastings. A 10-20 minute walk from the cathedral should bring you to a champagne cellar. I think that most cellars offer an English tour at some point during the day and a tasting at the end of the tour. I'm not sure of the cost, but it might be as little as $9.
Reims Cathedral has an impressive facade and Marc Chagall stained glass windows in the apse. The interior of the cathedral is about 455 ft. long, about 98 feet wide in the nave, and about 125 feet high in the center. It celebrated its 800th anniversary in 2011. Many French kings were crowned there.
The Porte Mars was built by the Romans in the 3rd Century, measures 32 meters in length with a height of 13 meters. It served as a city gate until 1544. It is located about a 6 minute walk from the train station and about 12 minutes from the cathedral.