This article includes a fine review of five leading derailleurs of the time Le Cyclo, Le Chemineau, Chemineau L’Izoard, the Boizot Le Montagnard and the Terrot Modèle HT.
The operation of the Boizot Le Montagnard appears to be roughly as follows. The cable pulls a spring-loaded lever with a vertical pivot. At the other end of this lever is a finger that moves the pulley cage along a rod.
(Source gallica.bnf.fr/ Bibliothèque nationale de France)