As far as I can ascertain, Stronglight were the first to offer square tapered BB spindles (and cranks to go with them) in 1933. In fact, this was Stronglight's first product. For detailed quotes, see Vintage Bicycle Quarterly No. 4, p. 4-5. These cranks quickly were adopted by the French cyclotourists, influenced by the technical trials, where these cranks proved their durability and performance.
There may have been others, but Herse is the second French one mentioned, introduced in 1938. See VBQ No. 4, p. 16-17.
Together with the alloy cranks (later called 49D), Stronglight also introduced a traditional steel crankset for cottered BBs (shown in the same ad in La Pedale Touristique quoted above). Racers didn't adopt the square tapered spindles until the 1950s, so Stronglight probably wanted to capture some of that market, too. I read somewhere (Le Cycliste, 1930s?) that the racers' reluctance was due to the higher Q factor of the alloy cranks (which by modern standards were super-low, but times change).
There were several attempts at splined BB axles. I have a Gnutti crankset from the 1950s (?). Anybody got an axle to go with that?
Jan Heine, Seattle Editor/Publisher Vintage Bicycle Quarterly http://www.mindspring.com/~heine/bikesite/bikesite/index.html