Champagne is the day trip least worth overthinking. The fastest TGV from Paris-Est reaches Reims in 46 minutes, the cathedral where French kings were crowned is free to enter, and the chalk cellars of the great houses lie a short walk or taxi ride away. Épernay, home of the Avenue de Champagne, is about 1 hour 20 minutes from Paris by direct train.
What a tour adds is the countryside: the vineyard villages and small family growers that are hard to reach without a car, plus someone else at the wheel. If you want the big-name cellars, go on your own by train. If you want vineyards and growers, book a small group. Both are covered below.