It really depends on what you want to do. You can take the train from Reims to Luxembourg, and then to Strasbourg. But you're not going to see a lot of "wine country" if you do that. The Champagne region runs east-west, and pretty much ends at Reims. The area from there into Luxembourg is more rolling hills and forest, with cattle. From Luxembourg to Strasbourg you cut across the Mosel Valley wine region and then into the Vosage Forest and come out into the Southern Rhine vineyards. And none of this will get you to "smaller" towns, as these are all larger cities.
The time of your trip is good. You'll be at the tail end of the harvest and into the crush. But do get a rental. Then, from Reims, drive west on the Champagne Road toward Chateau Thierry. You pass through a number of those smaller towns, most of them with smaller, less well know, champagne houses. That's where you find the really good deals. You may not get the polished tours you'll find in the famous cellars, but the wine can be fantastic. And it's a beautiful drive.
I can't see spending three days in Luxembourg, frankly it's one of those places I hate to drive in, and expensive. I prefer to spend my time in the Meuse-Argonne, walking over the old battlefields, sitting in small town cafes, and just sitting on a hillside watching to world go by. There are dozens of major monuments to past wars, the history runs very deep, and I really like driving the back roads. Take Varennes for example; it's an attractive smaller town, where King Louis XIV was captured as he tried to escape the revolution, where major battles were fought in 1870 and WWI, and where you can find a good regional meal for less than 20 euro. This is an area difficult to explore by train.
If you do go to Luxembourg, take the time to go north to Vianden and see the castle.
As for Strasbourg, it's okay, but again, it's expensive (figure 50 euro/day to park) and the smaller towns in the area surrounding the city are more geared towards wine than the city, which is the administrative hub of the EU. Lot's of folks on this board tend towards Colmar (to the south) but I like the area north towards Hagenau and the pottery villages. And, of course, the Maginot line and German Westwall fortifications from WWII.