French makers. Unfortunately I do know little of French makers in early days, but wooden "Régence" and "Staunton" sets have been made in France in the area around Saint Claude in the Jura in huge quantities, because boxwood was present in huge quantities. This was important for chess set manufacturing in the late 19th and 20th centuries. Henry Lardy, being the biggest, Henri Chavet, Michel Roz, Vauchier et fils and Jurabuis are all chess set manufacturers. Likely there were some more.
Lardy was founded in 1890 and situated in Dortan in the French Jura. Their dominance of chess set making was in period 1930ies till early 1970ies, when they sold their sets all over the world. Late 1980ies they stopped producing chess sets, because they couldn't compete with cheap sets from India. Apparently their shop closed in 1992. The Lardy pattern has been licensed to many other manufactures around the world. See for instance Hempfling “Staunton” (Germany) or Homas 20st century (Netherlands). Lardy chessmen were available felted and unfelted, as well as weighted and unweighted. They ranged in size from the small set with a 2-3/4” King, to large Club-size sets with King heights over 4-3/4”. Next to the Lardy pattern with it's characteristic Knight, they made also better quality sets with knights having glass eyes.
I do not know who made the Galalith "Régence" and "Staunton" sets in early 20th century. They are quite hard to find and I do not think they were mass produced. Pieces had to be turned and carved by hand and they usually come in a suitable cassette. And I wonder what the price of Galalith was in those days? Most likely these sets were already expensive at the time.