Low-carb diet and paleo diet advocates often align themselves, even though S. Boyd Eaton’s 1988 version of the paleo diet doesn’t appear to be very low-carb at all: 46% of total calories from carbohydrate. The standard American diet provides 50-55% of calories from carbohydrate. Paleo proponents and low-carbers do share an affinity for natural, whole foods, and an aversion to grains, milk, and legumes.
A 2010 article by Kuipers et al (reference below) sugggests that the East African Paleolithic diet derived, on average, 25-29% of calories from protein, 30-39% from fat, and 39-40% from carbohydrate. That qualifies as low-carb. Modern Western percentages for protein, fat, and carb are 15%, 33%, and 50%, respectively.
Loren Cordain and associates in 2000 suggested that Paleolithic diets may have derived about a third—22 to 40%—of calories from carbohydrate, based on modern hunter-gatherer societies.
You can make a good argument that these paleo concepts are healthy: high physical activity, nonsmoking, consumption of natural whole foods while minimizing simple sugars and refined starches. The paleo community is convinced that grains and legumes are harmful; many others disagree. Also debatable are the roles of dairy, polyunsaturated to saturated fat ratio, low sodium, and high potassium. Modern diets tend to be high-sodium and low-potassium, which may predispose to high blood pressure and heart trouble—diseases of modern civilization.
It appears that the average paleo diet may have derived about a third of calories from carbohydrate: that qualifies as low-carb.
Kuipers, R., Luxwolda, M., Janneke Dijck-Brouwer, D., Eaton, S., Crawford, M., Cordain, L., & Muskiet, F. (2010). Estimated macronutrient and fatty acid intakes from an East African Paleolithic diet British Journal of Nutrition, 1-22 DOI: 10.1017/S0007114510002679. Note that one of the authors is Loren Cordain. Good discussion of various Paleolithic diets.
Eaton, S., Konner, M., & Shostak, M. (1988). Stone Agers in the fast lane: Chronic degenerative diseases in evolutionary perspective. The American Journal of Medicine, 84 (4), 739-749 DOI: 10.1016/0002-9343(88)90113-1
Cordain, L., et al. Plant-animal subsistance ratios and macronutrient energy estimations in worldwide hunter-gatherer diets. American Journal of Clinical Nutrition, 71 (2000): 682-692.