My girlfriend and I are planning a two week vacation to Munich, Belgium, and France this fall. Not knowing much about France, we are looking for an area in northern France that we can see a few wineries. Specifically, we are looking for something that's not far from Belgium to minimize the time on the train to get there, reasonably affordable wine and accommodations (my understanding is that this rules out Champagne), and a reasonable distance from Paris or another major airport since we will be departing from France. Any suggestions would be appreciated.
Not knowing much about France, we are looking for an area in northern France that we can see a few wineries
Presumably you have an interest in wine, or else you wouldn't be planning to visit vineyards. As you suggest, Champagne is the closest wine producing area to Belgium, and there is also a small area in Alsace where Riesling is the commonest grape and many of the wines are similar to those you find in the German Rhineland. Colmar would be a good place to stay to tour this area, but if you like Riesling and similar wine then really you might as well do your vineyard visits in Germany, on route to Belgium.
Next closest, south west of Paris is the Loire valley, where white wine accounts for well over half of production. It's a very large, complex and varied area and thorough research would be required to pick the best places to visit - it's not all Chenin Blanc.
If I was particularly interested in visiting vineyards then first of all I'd want to go to the places where they make the wine I like, rather than what happened to be close by. Do you especially like northern French wines? In just over 2 hours from Paris by TGV you could be in Valence at the southern end of the northern Rhone region, and in about an hour more you could get to Orange, close to Chateauneuf-du-Pape in the southern Rhone. That's what I'd do, but then I'm not keen on northern wines.
I would go with Burgundy. Although more east central France, Dijon is only 1 1/2 hour from Paris on the TGV. I would recommend making a day of it and signing up for one of the many wine tours. A middle-of-the-road tour would be 63 euro pp for a half day tour in a van with 2 or 3 other couples with guide/driver, visiting a couple of wineries and at least one serious tasting session. They will pick you up not far from Dijon station, and drop you off in Beaune for lunch, and you can take an afternoon session for 53 euro for more touring and tastings. At the end of the day, they will drop you back at Dijon station for your train back to Paris. Not only fun , but educational. A very good primer on French, and especially Burgundy wines.
There are many tour companies who do this. We used "Wine and Voyages". http://wineandvoyages.com/home
Checking a little more into Champagne might reveal some affordable options - if you're not planning on buying Dom Perignon by the case or staying in the most expensive hotel in Reims. Our honeymoon in September 1999 was a 1-week bicycle tour starting and ending in Paris but pedaling thru the Champagne region. We used trains in a few places to cut travel time and avoid a couple of major hilly sections. It was harvest time, and we had to watch for agricultural vehicles and mud on the roads, but also got to stop a couple of times and clip & taste grapes being harvested. Tasting rooms had free champagne samples. It's been 14+ years, so perhaps things have changed considerably, but we found lodging and dining options that didn't cost an arm & a leg (we needed both legs for pedaling). We enjoyed touring Moet & Chandon in Epernay and just missed the last tour time of the day at Taittinger in Reims, but the region offers scenery, cuisine, and medieval architecture in addition to champagne wine.