Why are savory crepes from some restaurants brown?

I suspect that you're lucky enough to have had the proper savoury pancake from some regions of France (e.g. Brittany). This isn't known as a crepe in French, but as a galette. This word also has other meanings, as a type of cake, tart or biscuit (British English)/ small crisp cookie (US English). Wikipedia has an article discussing many types. French Wikipedia lists many more. Here's a related picture from Wikipedia for comparison:

Breton galettes, i.e. those of the pancake variety, are made using buckwheat flour which itself has a mild savoury flavour, not exactly nutty but in that direction. They're a greyish brown rather than the golden colour of crepe. French names for buckwheat flour include farine de sarrasin and farine de blé noir, the latter meaning black wheat/grain/corn flour. Fillings are savoury (various cheeses, ham, etc.); occasionally nuts and honey are used together with savoury ingredients. Traditionally, galettes are paired with sparkling cider.

Galettes are not widely found outside France. In fact, even in France they are not easy to find outside Brittany, Normandy, the Loire region and the Vendee. I have been able to get them in the UK in the past. I've never seen them in the US (checking your profile), but haven't tried to find them either.

Disclaimer: French, and lover of Crêpes and Galettes. I tried to find as many English links as possible, but some articles had no English translations and are therefore in French.

TL;DR

It was either a Crêpe au Sarrasin or Galette de Sarrasin.

Both are made from buckwheat (sarrasin, also called blé noir), which give them their brown color.

If it had a smooth surface, it was a Crêpe, whereas if the surface was pockmarked, it was a Galette.

The 3 cousins

There are 3 cousins:

• La Crêpe au Froment, from Lower Brittany, is the sweet kind, made with wheat flour.
• La Crêpe au Sarrasin, also from Lower Brittany, is the salty kind, made with buckwheat.
• La Galette de Blé Noir/Sarrasin, from Upper Brittany, is also the salty kind, also made with buckwheat, but not quite the same recipe.

The Crêpe au Froment is lightweight, such as the typical Crêpe Suzette, a Crêpe buttered up with some sugar sprinkled on top before being rolled or folded. They may also come with chocolate (Nutella or melted chocolate), jam, and even ice cream.

From Mizina / Getty, found on elle.fr.

The Crêpe au Sarrasin or Galette de Sarrasin are heartier, and come with more salty fillings: eggs, ham, cheese, fish, ...

From journaldesfemmes.fr, a Galette from the recipe.

Geography: the Lower/Upper Brittany are so named due to their elevation, in terms of geography the Lower Brittany is the Western part and the Upper Brittany the Eastern one.

Sarrasin: Crêpe or Galette?

The Crêpe au Sarrasin is a crêpe. While its preparation uses buckwheat, is also uses regular wheat flour, milk and eggs. The result is a finer, more brittle pancake with a smooth surface.

From Kampouz.com; Kampouz is Breton for Crêpe au Sarrasin.

The Galette de Sarrasin instead is prepared solely from water, buckwheat and salt. It yields a thicker, more flexible pancake with a pockmarked surface.

From cuisineaz.com, illustrating a recipe for crêpes.

Brown Crêpe or Galette?

Most people, even the French, do not quite make the difference between the Crêpe au Sarrasin and Galette de Sarrasin.

Even in a Crêperie, often founded by a Breton, or touting to have been, the name Crêpe may be used to refer to a Galette.

In my experience Crêperies tend to use the Galette de Sarrasin in preference to the Crêpe au Sarrasin; if you have allergies I'd advise checking with the staff just in case.

What's in a Crêpe?

It depends. Worse, due to the confusion between Crêpe au Sarrasin and Galette de Sarrasin the latter can also be referred to as Crêpe!

Contextual clues can be quite useful, though:

• If you see a street vendor, especially around Chandeleur, which sells crêpes, you'll get the froment kind. The lightweight nature of the crêpe, and its sweet and therefore sticky filling, makes them easy to eat on the go.
• If you walk into a crêperie, then crêpes will refer to both. You can check for clues in the menu: froment goes with sweet filling whereas blé noir/sarrasin goes with salty filling. It's quite likely you'll get a Galette de Sarrasin even if it's named Crêpe.

Other Galettes

Adding to the confusion, the name Galette is also used for:

• The Galette des rois (FR), also known as Galette Parisienne: a specialty of Epiphany in the northern part of France, which is a plate-sized cake filled with Pâte d'Amande (Almond Paste/Marzipan).
• The Galette Bretonne, or Breton Butter Biscuit: a palm-sized biscuit which leaves you with buttery fingers, which originated in Lower Brittany.

And just to make it more confusing, in Upper Brittany the term Galette Bretonne refers to Galette de Sarrasin; because why not?

Outside of old French traditions like the galettes discussed by Chris H, there are a ton of modern recipes for crepes made with different kinds of whole grain flour. It can be whole wheat, or any other grain or pseudograin. Most of them will be noticeably darker than a normal crepe made with white wheat flour.

So it is impossible to say which one exactly was that you ate. If you are so inclined, you can gather several different whole grain recipes and test them, and see which one reminds you most of the crepe you were served, or maybe which one you like most - sounds like a very fun experiment to me. Don't forget to also include "atypical" gluten free flours such as teff or plantain, they tend to take the conversion quite well and produce a nice variety of results.

The darkness and sweet/savory thing are not related, if you want it and sweet, choose a recipe with sugar, for savory take one without sugar. I basically never add sugar to my crepes, they become sweet when I use sweet fillings.