"This entire wall used to be lined with wine barrels," said Genevieve Lahaye, a winemaker in Pommard, at the heart of Burgundy. She was gesturing toward a long wall in June, speaking through a translator as she rubbed her careworn hands and explained the woes of a landowning vintner amid the region's recent years of disastrous weather. A mere three barrels were lined up, though the wall at Domaine Lahaye looked as if it could hold more than a dozen.

This is the new normal for smaller winemakers in the legendary wine region, just a few hours' drive southeast of Paris. For the past few years, hail, frosts, and too much rain at times have resulted in yields of fewer than half the grapes of a good harvest. Last spring, multiple late frosts hit the Côte de Beaune, the central stretch of the ribbon of stony slope where Burgundians grow wine. Hailstorms, too, have crushed the area. As a result, 2016 may be one of the smallest harvests ever.

Which is why this is the perfect time to visit as a tourist to check out the rest of what Burgundy has to offer—and to support smaller wineries and businesses that are struggling in the face of poor weather conditions earlier this year.

Although travel agents and wine experts are warning tourists that individual vineyards may not have product to dish out for tastings, the wine that has been squeezed out of those difficult seasons is incredibly good, if you can get your hands on it. It displays the complexity and structure for which the region is renowned, born in limestone-studded soil and grapes that struggle for life along the hills.

"2016 will be the shortest harvest that they’ve had in the last 25 years. It depends on where you are, but some vineyards were devastated," explained Geoffrey Troy of New York Wine Warehouse, which imports both ultra-high-end and mid-market Burgundies. "But it’s not over for them. The 2015 is an extraordinary vintage for red, and 2014 is an extraordinary vintage for white and a very good vintage for red. If we miss a year, I can see the prices going up, but I don’t see us running out of wine. There’s plenty in the pipeline."

Plus, there's plenty to do in the region beyond chasing grape juice.

How to Do Burgundy, Now

First things first: Rent a car.

One of the great pleasures of a truly gorgeous wine region is driving through the vineyards in the late afternoon light. There's nothing like the way the low sun illuminates the golden, green leaves—plus, on this trip you will want to be able to cover a lot of terrain easily. Burgundy is a confusing warren of tiny plots of vines, assigned hundreds of years ago by Cistercian monks. To experience the breadth of the wines, you are going to want to see a lot of the region.

Burgundy, not known for luxury resorts, ends up being mostly a destination for serious oenophiles. More general wine tourists are likely to be steered elsewhere by travel agents.

"There's a great value going to France now, and the crowds have thinned," explained Judy Stein of Ovation travel, which handles corporate and ultra-VIP travel. "People are going to go to Burgundy because of the passion to go—if they’re serious, serious wine connoisseurs—versus other areas where people are interested in having a wine experience combined with a comfortable property."

During a recent visit, I stayed with friends in a perfectly renovated 17th century stone barn in the Chardonnay-drenched town of Meursault. The property overlooked a small parcel of vineyards and had been painstakingly converted into rental apartments (going for about $2,000 a week). More than a hundred such properties are dotted through the charming villages of the Côte de Beaune and Côte de Nuits.

Wandering up twisted streets among stone walls threaded with blossoming rose vines, it felt like the best way to experience provincial town life. In the morning, you grab a pastry at the boulangerie on the impeccably charming town square, and then a coffee at the restaurant-slash-grocery-slash-bar in which the locals seem to hang out all day. You admire the colorful tile roofs on the teetering town hall, straight out of Beauty and the Beast, taking a moment to relax. Then you wander home, get in the car, and start your day.

There are dozens of comparable towns you could call home base, so when scouring the Internet, look at Pommard, Santenay, Flavigny, Puligny-Montrachet, and Volnay if you want to be among the vines. For a more traditional hotel experience, the wine crew tends to pick L'Hotel de Beaune (rooms start at $427 a night) and Hotel de Cep (rooms start at $396).

What to Do

A bike tour of the Côte de Beaune was my first trek on a visit in June ($40 per person). Our guide was the first of many to try to explain the internecine, archaic way by which wine is classified in the region as we stopped to taste bottles along the way. Even if you think you will never understand it, locals do their best to drill the system into your head.

As we looked down from the hillside in Volnay, we were told about the premier and grand cru vines that grew near the top of the ridge above us, the third-tier "Village" wines grown around us, and the low patches of land that are allowed to generate only what the locals think of as generic plonk (Vins de Bourgogne) down in the flatlands of the valley. To me, even those were quite tasty.

Even without the wine history, a bike ride is a perfect way to explore the hillside: Dozens of tiny, quiet roads trace along the slope and between towns that are each more picturesque than the last. Even if you get caught in the rain (as we did, hiding under a centuries-old roof in the blossom-filled courtyard at Domaine Lahaye) you will have a muddy good time.

A historical tour is also in order, as some of those medieval towns are nearly too cinematically cute to be real. Authentica Tours or Burgundy Discovery Tours offer trips to multiple towns, where well-informed guides will help you cover a lot of terrain in an afternoon or full day. The towns of Semur-en-Auxois, with ancient towers and hilltop town square, and Flavigny-sur-Ozerain—where the movie Chocolat was filmed—are worth an afternoon's wandering.

Be sure to make time for a self-guided tour of the breathtaking Abbey de Fontenay, the historically compelling Cluny Abbey—where a clever 3D digital restoration helps long-lost buildings come alive—and the sumptuous Hospices de Beaune, with their steep, glazed-tile roofs and overly ambitious audio tour.

Wine-Related Treats

So you want to do some wine tourism? Schedule a visit to one of the many negociant shops in Beaune, Dijon, Chablis, or smaller towns to learn the best array of what's available. Keep in mind that many of them charge for tastings, and most have wines they want to hawk. Despite the shortage of wine, some of the larger organizations, such as Patriarche in Beaune, are running in normal fashion and host tastings all day. But you will be warmly welcomed anywhere you go if you have arranged a visit and offered to pay to taste.

Still, the best experiences for a novice wine traveler relate to food and exploration.

If you check in a few weeks in advance, you can arrange a seat at one of Christine Drouhin's intimate, vineyard-side luncheons at Domaine Drouhin-Laroze. The lady of the winery home-cooks such Burgundian delights as boeuf bourguignon and the best Gruyere potatoes au gratin you have ever tasted. She will offer you half-bottles of the winery's mildly spicy reds to accompany the various courses and then lead you on a private tour of the centuries-old wine cellars.

In the wine capital of Beaune, reach out to Domaine Chanson to set up a visit to the gorgeous 18th century mansion near the edge of town. Tour their cool, spiraling wine cellars, which fill a hollowed-out tower that was once part of the ancient city walls. Some rooms date back to the 13th century.

The warm and knowledgeable Catherine Goutorbe will guide you through a tasting of recent highlights such as the garnet-colored Beaune-Bastion Premier Cru 2013, with its dark cherry notes and full body, or the incredible Corton Vergennes Grand Cru 2013, a powerful-for-France Chardonnay with just the right amount of oak.

Where to Eat

With all your drinking and exploring, it's important not to forget to indulge in Burgundy's world-renowned cuisine. You'll not regret making ample time for long lunches and dinners, tasting the local village wine (so you don't break the bank, even as you destroy your diet). Here are some recommendations:

Ma Cuisine: This cafe near the historic center of Beaune is a mecca for winemakers and oenophiles, who assemble there to explore the magnificent wine list and share bottles. Show up early and chat up your neighbors for the latest local gossip, while dining on solid Burgundian fare.

Le Chevreuil: In the tiny, cinematic hamlet of Meursault, this contemporary French restaurant features a hip menu of farm-fresh delights, plus a quiet deck that overlooks vineyards and a beautiful château on the edge of town.

Le Centre: If you are looking for a more traditional experience, sign up for a long evening at Le Centre, just off the historic town square in Meursault. Top-notch Burgundy cooking (think duck, boeuf bourguignon, and oeufs en meurette) combines with a convivial atmosphere; by the end of your meal, dogs that seem to belong to the whole town will be bounding between tables looking for snacks, and neighbors will take turns pouring one another wine and telling stories. Just don't expect to get out quickly—here, speed comes in a distant third, after atmosphere and taste.

L'Episode: Operating out of the back of a beloved specialty shop (La Petite Vadrouille) in Meursault, the young couple behind this catering company and teensy terrace restaurant are devoted to serving meals that feel both very modern and home-cooked. Fresh local ingredients and longstanding tradition combine for a unique, private experience at L'Episode.

Le Petit Roi de la Lune: Located just off Dijon's impressive Place de la Liberation, this little restaurant occupies the ground floor of one of the city's oldest houses. It specializes in local comfort food such as escargot, fried Camembert, and steak with Saint-Marcellin cheese.